WO2015043385A1

WO2015043385A1 - Method and apparatus for reducing network flow graph

Info

Publication number: WO2015043385A1
Application number: PCT/CN2014/086482
Authority: WO
Inventors: 王蕾; 崔慧敏; 冯晓兵
Original assignee: 华为技术有限公司
Priority date: 2013-09-29
Filing date: 2014-09-15
Publication date: 2015-04-02
Also published as: CN104516995A

Abstract

Embodiments of the present invention provide a method and an apparatus for reducing a network flow graph. The method comprises: obtaining first network flow subgraphs from a to-be-processed network flow graph, the first network flow subgraphs comprising M nodes and edges between the M nodes, and the M nodes comprising a first endpoint; combining the first network flow subgraphs into a first node; and forming a first reduction network flow graph by the first node and second network flow subgraphs except the first network flow subgraphs in the to-be-processed network flow graph, a capacity (a maximum flow value) of a minimum cut of the first reduction network flow graph being equal to a capacity (a maximum flow value) of a minimum cut of the to-be-processed network flow graph, and the first node being a first endpoint of the first reduction network flow graph, so that a scale of a graph can be effectively reduced. According to the embodiments of the present invention, a to-be-processed network flow graph does not need to conform to a certain rule, so that a process of reducing a scale of a graph has universal applicability.

Description

Network flow graph reduction method and device

The present application claims priority to Chinese Patent Application No. 201310456975.0, entitled "Network Flow Map Reduction Method and Apparatus", filed on Sep. 29, 2013, the entire disclosure of which is incorporated herein by reference. .

Technical field

The embodiments of the present invention relate to the field of graph theory and combination optimization of algorithms, and in particular, to a network stream graph reduction method and apparatus.

Background technique

The maximum flow minimum cut problem is a classic problem in graph theory and combinatorial optimization, such as local community discovery of social networks, Sybil attack defense system, online content voting system, Google's advertising system, spam discovery, computer vision, VLSI layout design. Applications such as aircraft flight schedules and DNA multi-sequence comparisons can be modeled as maximum flow minimum cut algorithms. The maximum flow is the maximum flow of each edge between the nodes in a directed graph, wherein the maximum flow from the source node is the maximum flow of the directed graph, and the maximum flow into the junction is the For the maximum flow to the graph, the inflow of the remaining nodes is equal to the outflow, and the flow rate of each edge between the nodes cannot exceed the capacity limit. In the directed graph, some edges are removed, so that the directed graph becomes two unconnected subgraphs, and the source point and the sink point are respectively in different subgraphs, and each subgraph can be called a cut, removed. The sum of the flows of these edges is the cut capacity, the minimum cut is the cut with the smallest cut capacity, and the maximum flow value is equal to the minimum cut capacity. When the size of the directed graph is large, the maximum flow minimum cut algorithm is used to find the maximum flow minimum cut time is very long.

In the prior art, the scale of the directed graph can be reduced by reducing the number of nodes and edges in the directed graph, that is, the method based on the node pattern matching is used to reduce the scale of the directed graph, that is, to observe the directed graph. The structure, if some of the nodes' patterns conform to the preset mode, the nodes can be combined into one node, thereby reducing the scale of the directed graph.

However, the method based on node pattern matching is only applicable to the fields of computer vision and theoretical physics. It can only process rule diagrams with special structure, cannot handle irregular directed graphs, and has poor applicability.

Summary of the invention

The embodiment of the invention provides a network flow graph reduction method and device, which is used for effectively reducing the scale of the graph, and does not require the network flow graph to be processed to meet certain rules, so that the process of reducing the scale of the graph has universal applicability.

In a first aspect, an embodiment of the present invention provides a network flow graph reduction method, including: acquiring a first network stream submap from a to-be-processed network flow graph, where the first network stream submap includes M nodes and M An edge between nodes, wherein the M nodes include a first endpoint, the M is an integer greater than or equal to 2, and the to-be-processed network flow graph includes N nodes and N nodes The N nodes include a source node and a sink node, the N is an integer greater than M, the first endpoint is a source node or a sink node, and the source node is used a starting node of the network flow indicating the network flow graph to be processed, the sink point being an end node of the network flow, wherein an edge between each node represents a network between each node Flow relationship

Combining the first network stream submap into a first node;

Forming, by the first node, a second network stream submap other than the first network stream submap in the to-be-processed network flow graph to form a first reduced network flow graph, where the second network proxy submap is Determining, in the processing network flow graph, all remaining nodes except the first network stream submap and edge components between the remaining nodes; all nodes and locations of the first network stream submap An edge between all nodes of the second network stream submap becomes an edge between the first node and all nodes of the second network stream submap, and the first reduced network flow graph includes a first node, the second network stream submap, and an edge between the first node and all nodes of the second network stream submap, the minimum of the first reduced network flow graph The cut capacity is equal to the minimum cut capacity of the to-be-processed network flow graph, and the first node is the first endpoint of the first reduced network flow graph.

In a first possible implementation manner of the first aspect, the combining the first part of the to-be-processed network flow diagram into a first node includes:

Removing the edge between the M nodes of the first network stream submap;

The M nodes are aggregated into one of the first nodes.

With reference to the first aspect, or the first possible implementation manner of the first aspect, in the second possible implementation manner of the first aspect, the obtaining, by the network flow graph to be processed, the first network flow sub-map includes:

Starting from the first endpoint, searching for a third network stream submap including a preset number of nodes, The third network stream submap includes an edge between the preset number of nodes acquired by the search and the preset number of nodes acquired by the search, where the preset number is greater than or equal to The M;

Merging the fourth network stream submap other than the third network stream submap in the to-be-processed network flow graph into a second node, where the fourth network stream submap is used by the to-be-processed network stream Removing all remaining nodes except the third network stream submap and edge components between the remaining nodes except the third network stream submap;

Forming, by the second node and the third network stream submap, a fifth network stream submap, where all nodes of the fourth network stream submap and all nodes of the third network stream submap An edge between the second node and all nodes of the third network stream submap, the fifth network stream submap including the second node, the third network a stream submap and an edge between the second node and all nodes of the third network stream submap, the second node being a second endpoint of the fifth network stream submap;

Wherein, when the first endpoint is a source node, the second endpoint is a sink node, and when the first endpoint is a sink node, the second endpoint is a source node;

And determining, according to the minimum cut partition of the fifth network stream submap, the first minimum cut subgraph of the fifth network stream submap as the first network stream submap.

With reference to the second possible implementation manner of the first aspect, in a third possible implementation manner of the foregoing aspect, the fifth network flow according to the minimum cut partition of the fifth network stream submap After the first minimum cut subgraph of the subgraph is used as the first network stream submap, the method further includes:

Restoring the second node to the fourth network stream submap, and the edge between the second node and all nodes of the third network stream submap becomes the fourth network stream submap The edge between all nodes and all nodes of the third network stream submap.

In conjunction with the first aspect or the first possible implementation of the first aspect or the second possible implementation of the first aspect or the third possible implementation of the first aspect, the fourth possibility in the first aspect In the implementation manner, after the first node and the second network stream submap other than the first network stream submap in the to-be-processed network flow graph form a first reduced network flow graph, the method further includes :

Recording the reduced number of times of the to-be-processed network flow graph to obtain a reduced number of times of the to-be-processed network flow graph.

With the fourth possible implementation of the first aspect, in a fifth possible implementation manner of the first aspect, if the number of times of the network flow graph to be processed is smaller than the first preset number of times, The first reduced network flow graph is updated to the to-be-processed network flow graph.

With the fifth possible implementation manner of the first aspect, in a sixth possible implementation manner of the first aspect, if the number of times of the to-be-processed network flow graph is not smaller than the first preset number of times, The method also includes:

Obtaining a sixth network stream submap from the first reduced network flow graph, where the sixth network stream submap includes edges between K nodes and K nodes, where K is greater than or equal to 2 An integer, wherein the K nodes include a second endpoint, wherein when the first endpoint is a source node, the second endpoint is a sink node, and when the first endpoint is a sink node The second endpoint is a source node;

Combining the sixth network stream submap into a third node;

Forming, by the third node, a seventh network stream sub-picture other than the sixth network stream sub-picture in the first reduced network flow graph to form a second reduced network flow graph, where the seventh network flow sub-graph is configured by Removing, in the first reduced network flow diagram, all remaining nodes except the sixth network stream submap and edge components between the remaining nodes except the sixth network stream submap; An edge between all nodes of the sixth network stream submap and all nodes of the seventh network stream submap becomes all nodes of the third node and the seventh network stream submap The second reduced network flow graph includes the seventh network stream submap, the third node, and all nodes of the third node and the seventh network stream submap Between the edges, the minimum cut capacity of the second reduced network flow graph is equal to the minimum cut capacity of the first reduced network flow graph, and the third node is the second reduced network flow graph Two endpoints.

With reference to the sixth possible implementation manner of the first aspect, in a seventh possible implementation manner of the first aspect, the third node and the first reduced network flow graph except the sixth network After the seventh network stream submap outside the stream submap constitutes the second reduced network flow graph, the method further includes:

Recording the number of reductions of the first reduced network flow graph to obtain a reduced number of times of the first reduced network flow graph.

In conjunction with the seventh possible implementation of the first aspect, in an eighth possible implementation manner of the first aspect, if the reduced number of times of the first reduced network flow graph is less than a second preset number of times, The second reduced network flow graph is updated to the first reduced network flow graph.

In a second aspect, an embodiment of the present invention provides a network flow graph reduction device, including:

An acquiring unit, configured to obtain a first network stream sub-picture from a to-be-processed network flow graph, where the first network stream sub-picture includes an edge between the M nodes and the M nodes, where the M nodes are Including a first endpoint, the M is an integer greater than or equal to 2, and the to-be-processed network flow graph includes N junctions An edge between the point and the N nodes, wherein the N nodes include a source node and a sink node, the N is an integer greater than M, and the first endpoint is a source node or a sink node The source node is a starting node of the network flow for indicating the network flow graph to be processed, and the sink node is an ending node of the network flow, wherein an edge between each node Indicates the network flow relationship between nodes;

a merging unit, configured to merge the first network stream sub-graph obtained by the acquiring unit into a first node;

a processing unit, configured to combine the first node obtained by combining the merging unit with a second network stream submap other than the first network stream submap in the to-be-processed network flow graph to form a first reduced network flow The second network stream submap is composed of all remaining nodes except the first network stream submap and edges between the remaining nodes in the to-be-processed network flow graph; An edge between all nodes of the first network stream submap and all nodes of the second network stream submap becomes between the first node and all nodes of the second network stream submap Edge, the first reduced network flow graph includes the first node, the second network stream submap, and between the first node and all nodes of the second network stream submap The minimum cut capacity of the first reduced network flow graph is equal to the minimum cut capacity of the to-be-processed network flow graph, and the first node is the first endpoint of the first reduced network flow graph.

In a first possible implementation manner of the second aspect, the merging unit is specifically configured to remove an edge between the M nodes of the first network stream submap and aggregate the M nodes Is one of the first nodes.

With reference to the second aspect or the first possible implementation manner of the second aspect, in a second possible implementation manner of the second aspect, the acquiring unit is specifically configured to start from the first endpoint, and the search acquisition includes a third network stream submap of the preset number of nodes, where the third network stream submap includes the preset number of nodes acquired by the search and the preset number of nodes obtained by the search Between the edges, the preset number is greater than or equal to the M; and merging the fourth network stream submaps other than the third network stream submap in the to-be-processed network flow graph into one second a node, the fourth network stream submap is removed from all remaining nodes except the third network stream submap in the to-be-processed network flow graph, and the removing the third network stream submap Composing an edge between all remaining nodes; and forming the second node and the third network stream sub-picture into a fifth network stream sub-picture, all nodes and locations of the fourth network stream sub-picture An edge between all nodes of the third network stream submap becomes the second node and the third network stream An edge between all nodes of the subgraph, the fifth network stream submap including the second node, the third network stream submap, and the second node and An edge between all nodes of the third network stream submap, the second node being a second endpoint of the fifth network stream submap; wherein, when the first endpoint is a source node The second endpoint is a sink node, and when the first endpoint is a sink node, the second endpoint is a source node; according to the minimum cut of the fifth network stream submap, The first minimum cut subgraph of the fifth network stream submap is used as the first network stream submap.

In conjunction with the second possible implementation of the second aspect, in a third possible implementation of the second aspect, the method further includes:

a restoring unit, configured to: after the obtaining, the first minimum cut sub-graph of the fifth network stream submap as the first network stream submap according to the minimum cut partition of the fifth network stream submap Restoring the second node to the fourth network stream submap, and the edge between the second node and all nodes of the third network stream submap becomes the fourth network stream submap The edge between all nodes and all nodes of the third network stream submap.

In conjunction with the second aspect or the first possible implementation of the second aspect or the second possible implementation of the second aspect or the third possible implementation of the second aspect, the fourth possibility in the second aspect In the implementation, it also includes:

a first recording unit, configured by the processing unit to form, by the first node, a second network stream submap other than the first network stream submap in the to-be-processed network flow graph to form a first reduced network flow graph Then, the number of times of reduction of the to-be-processed network flow graph is recorded, and the number of times of reduction of the to-be-processed network flow graph is obtained.

In conjunction with the fourth possible implementation of the second aspect, in a fifth possible implementation of the second aspect, the method further includes:

a first updating unit, configured to update the first reduced network flow graph to the to-be-processed if the number of times of reduction of the to-be-processed network flow graph obtained by the first recording unit is less than a first preset number of times Network flow diagram.

With the fifth possible implementation of the second aspect, in a sixth possible implementation manner of the second aspect, if the number of reductions of the to-be-processed network flow graph obtained by the first recording unit record is not less than The acquiring unit is further configured to obtain a sixth network stream submap from the first reduced network flow graph, where the sixth network stream submap includes K nodes and K nodes. Between the edges, the K is an integer greater than or equal to 2, and the K nodes include a second endpoint, wherein when the first endpoint is a source node, the second endpoint is a sink a node, when the first endpoint is a sink node, the second endpoint is a source node;

The merging unit is further configured to merge the sixth network stream submap obtained by the acquiring unit into a third node;

The processing unit is further configured to combine the third node obtained by combining the merging unit with a seventh network stream submap other than the sixth network stream submap in the first reduced network flow graph. Diluting a network flow graph, wherein the seventh network stream submap removes all remaining nodes except the sixth network stream submap from the first reduced network flow graph and the removing the sixth network stream a side between all remaining nodes except the sub-picture; the edge between all the nodes of the sixth network stream sub-picture and all the nodes of the seventh network stream sub-picture becomes the third An edge between the node and all nodes of the seventh network stream submap, the second reduced network flow graph including the seventh network stream submap, the third node, and the third An edge between the node and all nodes of the seventh network stream submap, and a minimum cut capacity of the second reduced network flow graph is equal to a minimum cut capacity of the to-be-processed network flow graph, the first The third node is the second endpoint of the second reduced network flow graph.

In conjunction with the sixth possible implementation of the first aspect, in a seventh possible implementation of the first aspect, the method further includes:

a second recording unit, configured by the processing unit to form the third node and the seventh network stream submap other than the sixth network stream submap in the first reduced network flow graph to form a second reduced network stream After the figure, the number of reductions of the first reduced network flow graph is recorded, and the number of reductions of the first reduced network flow graph is obtained.

In conjunction with the seventh possible implementation of the second aspect, in an eighth possible implementation manner of the second aspect, the method further includes:

a second updating unit, configured to update the second reduced network flow graph to the first if the number of times of reduction of the first reduced network flow graph obtained by the second recording unit record is less than a second preset number of times A reduced network flow graph.

The network flow graph reduction method and apparatus provided by the embodiment of the present invention obtains the first network stream submap from the to-be-processed network flow graph, and then merges the first network stream submap into a first node, and then the first The second network stream sub-picture in the node and the to-be-processed network flow diagram except the first network stream sub-graph constitutes a first reduced network flow graph, and the minimum cut capacity of the first reduced network flow graph is equal to the to-be-processed network flow graph. The minimum cut capacity, the first node is the first end point of the first reduced network flow graph. By merging the first network stream submap of the M nodes including the first endpoint into the first node, the first node becomes the first endpoint of the reduced first reduced network flow graph, which is effective The size of the map is reduced, and the network flow graph to be processed does not need to meet certain rules, so that the scale of the map is reduced. The process has universal applicability.

DRAWINGS

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, a brief description of the drawings used in the embodiments or the prior art description will be briefly described below. Obviously, the drawings in the following description It is a certain embodiment of the present invention, and other drawings can be obtained from those skilled in the art without any creative work.

1 is a flowchart of Embodiment 1 of a network flow graph reduction method according to the present invention;

2 is a flowchart of Embodiment 2 of a network flow graph reduction method according to the present invention;

3 is a schematic diagram of a network flow graph to be processed according to an embodiment of the present invention;

4 is a schematic diagram of a first sub-picture provided by an embodiment of the present invention;

FIG. 5 is a schematic diagram of a first sub-picture including a first node according to an embodiment of the present invention; FIG.

FIG. 6 is a schematic diagram of a first reduced network flow diagram according to an embodiment of the present invention;

7 is a flowchart of Embodiment 3 of a network flow graph reduction method according to the present invention;

8 is a flowchart of Embodiment 4 of a network flow graph reduction method according to the present invention;

9 is a flowchart of Embodiment 5 of a network flow graph reduction method according to the present invention;

10 is a schematic structural diagram of Embodiment 1 of a network flow graph reduction device according to the present invention;

11 is a schematic structural diagram of Embodiment 2 of a network flow graph reduction device according to the present invention;

12 is a schematic structural diagram of Embodiment 3 of a network flow graph reduction device according to the present invention;

FIG. 13 is a schematic structural diagram of Embodiment 4 of a network flow graph reduction device according to the present invention.

detailed description

The technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. It is a partial embodiment of the invention, and not all of the embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative efforts are within the scope of the present invention.

FIG. 1 is a flowchart of Embodiment 1 of a network flow graph reduction method according to the present invention. As shown in FIG. 1 , the method in this embodiment may include:

S101. Acquire a first network stream submap from the to-be-processed network flow graph.

Including M nodes of the first endpoint, M is an integer greater than or equal to 2, and the first endpoint is to be The source node or sink node of the network flow graph.

In this embodiment, the network flow graph to be processed is a directed graph and a flow graph of the network flow, and the to-be-processed network flow graph includes edges between N nodes and N nodes, and N nodes are network flows. Each node passing through, the edge between each node represents the network flow relationship between the nodes, the N nodes include the source node and the sink node, and the source node is used to represent the network flow to be processed. The starting node of the network flow of the graph, the sink node is the ending node of the network flow of the network flow graph to be processed, and each side has capacity, and the network flow graph can be used to simulate the traffic volume of the road system and the pipeline. The liquid, the current in the circuit, etc., for example, the side in the network flow diagram can be a water pipe, the network flow is the water in the water pipe, the capacity of the side is the capacity of the water pipe, the source of the water flow serves as the source node, and the sink of the water flow Point as the sink point, the point where any water pipe meets is the node in the network flow graph except the source node and the sink node. That is, the network flows in the network flow graph are all flowing out from the source node, and the network flows in the final network flow will all flow into the sink node, and the edges between the two nodes in the flow direction relationship have a capacity, so The traffic of the network flow flowing on the edge cannot exceed the capacity of the edge, and the maximum traffic of the network flow flowing from the source point is the maximum flow of the to-be-processed network flow graph, and then the minimum cut capacity of the to-be-processed network flow graph The same as the maximum flow of the to-be-processed network flow graph.

The embodiment may be configured to include a first network stream submap, where the first network stream submap includes M nodes, where M is an integer greater than or equal to 2, and the M nodes include a first endpoint, and the first endpoint It may be a source node or a sink node of a network flow graph to be processed, where N is an integer greater than or equal to M. For example, the acquired first network stream submap may include a source node of the to-be-processed network flow graph, and the obtained first network stream submap may also include a sink node of the to-be-processed network flow graph.

S102. Combine the first network stream submap into a first node.

In this embodiment, after acquiring the first network stream submap, the first network stream submap is merged into a first node, for example, the first network stream submap is reduced to a node.

Optionally, combining the first network stream submap into a first node may include: removing an edge between the M nodes of the first network stream submap; and aggregate the M nodes into a first node. Node, specifically, removing the edge between the M nodes of the first network stream sub-picture, it can be considered that the network flow relationship between the M nodes does not exist, and then the M nodes are aggregated into one node. Point, this node is called the first node.

S103. The first network and the second network stream sub-picture except the first network stream sub-picture in the to-be-processed network flow graph are formed into a first reduced network flow graph, where a minimum cut capacity of the first reduced network flow graph is equal to The minimum cut capacity of the network flow graph to be processed, the first node is the first of the first reduced network flow graph End point.

In this embodiment, the network flow graph except the first network stream submap in the to-be-processed network flow graph may be referred to as a second network stream submap, and the second network stream submap is removed from the to-be-processed network flow graph. All remaining nodes except a network stream sub-picture and the edges between all the remaining nodes; may be based on all nodes of the first network stream sub-picture and all nodes of the second network stream sub-picture The edge becomes the edge between the first node and all the nodes of the second network stream sub-picture, and the second network stream sub-picture other than the first network stream sub-picture in the to-be-processed network flow picture is merged with the foregoing The first node constitutes a network flow graph, and the formed network flow graph is referred to as a first reduced network flow graph, and the obtained first reduced network flow graph includes a first node, a second network stream submap, and the first The edge between the node and all the nodes of the second network stream submap; if the first endpoint included in the first network stream subgraph obtained in S101 is the source point, then the first node becomes the first Reducing the source point of the network flow graph; if the first network stream submap obtained in S101 is included End point is the sink node, the first node becomes the first sink down stream network of FIG.

It should be noted that the minimum cut capacity of the first reduced network flow graph obtained by the above steps in this embodiment is equal to the minimum cut capacity of the network flow graph to be processed, and the first reduced network flow obtained through the above steps. The maximum flow of the graph is equal to the maximum flow of the network flow graph to be processed. Thus, the maximum flow minimum cut of the first reduced network flow graph is equivalent to the maximum flow minimum cut of the pending network flow graph.

Embodiment 1 of the present invention provides a network flow graph reduction method, which obtains a first network stream submap from a to-be-processed network flow graph, and then merges the first network stream submap into a first node, and then the first node. And the second network stream submap except the first network stream submap in the to-be-processed network flow graph constitutes a first reduced network flow graph, and the minimum cut capacity of the first reduced network flow graph is equal to the minimum of the to-be-processed network flow graph The cut capacity, the first node is the first end point of the first reduced network flow graph. By merging the first network stream submap including the M nodes into the first node, the first node becomes the first endpoint of the reduced first reduced network flow graph, which can effectively reduce the scale of the graph. There is no need to process the network flow graph to meet certain rules, so that the process of reducing the scale of the graph has universal applicability.

2 is a flowchart of Embodiment 2 of a network flow graph reduction method according to the present invention. As shown in FIG. 2, the method in this embodiment may include:

S201. Starting from the first endpoint, searching for a third network stream submap including a preset number of nodes.

In this embodiment, starting from the first endpoint of the to-be-processed network flow graph, performing a search along the edge between the node and the node to obtain a third network stream submap including a preset number of nodes, where The preset number of nodes includes a first endpoint, and the third network stream submap obtained by the search includes an edge between the preset number of nodes obtained by the search and the preset number of nodes obtained by the search. The preset number may be determined according to the actual application scenario, and the embodiment of the present invention is not limited herein. For example, you can start from the sink point and use the Breadth First Search (BFS) method to search the network flow graph to obtain the preset number of nodes including the sink node. Network stream submap. For example, starting from the source node, the BFS method is used to search the network flow graph to obtain a third network stream submap of the node of the preset data including the source node. It should be noted that the BFS method and the reverse BFS method are consistent with the prior art, and the embodiments of the present invention are not described herein again.

3 is a schematic diagram of a network flow graph to be processed according to an embodiment of the present invention. As shown in FIG. 3, the network flow graph to be processed has

numbers

0, 1, 2, 3, 4, 5, 6, and 7. The nodes of 8, 9, and 10, wherein the node numbered 0 is the source node, the node numbered 10 is the sink node, and the line with the arrow is the network flow direction between the node and the node. The edge, the number on the side represents the capacity of the network stream on the edge, that is, the maximum flow allowed to flow. If the preset number is 7, then it starts from the junction point (that is, the node numbered 10). Using the reverse BFS method to search, you can search for the node numbered 7, the node numbered 8, the node numbered 9, the node between the number 7 and the node numbered 10, The edge between the node numbered 8 and the node numbered 10, and the edge between the node numbered 9 and the node numbered 10, and then the reverse BFS is used from the node numbered 7 Method Search, you can search for the node numbered 4, and the edge between the node numbered 7 and the node numbered 5; the reverse B is used from the node numbered 8 The FS method searches to find the node numbered 5, and the edge between the node numbered 8 and the node numbered 5; the node with the number 9 starts the search using the reverse BFS method. You can search for the node numbered 5, the node numbered 6, the edge between the node numbered 5 and the node numbered 9, and the node numbered 9 and the node numbered 6. The edge between the two, so that a network stream sub-graph can be obtained, the network stream sub-picture includes 7 nodes including the node numbered 10 and the edge between the 7 nodes, respectively, the 7 nodes respectively For nodes numbered 4, 5, 6, 7, 8, 9, and 10.

S202. Combine, in the network flow graph to be processed, the fourth network stream submap other than the third network stream submap into a second node.

In this embodiment, the network flow graph except the third network stream submap in the to-be-processed network flow graph is used as the fourth network stream submap, and the fourth network stream submap is removed from the to-be-processed network flow graph to remove the third network. The remaining nodes other than the stream subgraph and the edges between the remaining nodes except the third network stream subgraph are composed.

Optionally, combining the fourth network stream submap into a second node may include: removing edges between all nodes in the fourth network stream submap; and all nodes of the fourth network stream submap Point aggregation is a first node. Specifically, the edge between all nodes in the fourth network stream submap is removed. It can be considered that the network flow relationship between all nodes in the fourth network stream submap is not It exists, and then all the nodes in the fourth network stream subgraph are aggregated into one node, which is called the second node.

S203. The second node and the third network stream sub-picture are combined into a fifth network stream sub-picture.

In this embodiment, the second node and the third network stream may be formed according to an edge between all nodes of the fourth network stream submap and all nodes of the third network stream submap. The edge between all the nodes of the graph forms a network flow graph with the second node and the third network stream submap described above, and the formed network flow graph is called a fifth network stream submap, and the obtained fifth network is obtained. The stream subgraph includes a second node, a third network stream sub-picture, and an edge between the second node and all nodes of the third network stream sub-picture, and the second node is a fifth network stream sub-picture The second endpoint.

Wherein, when the first endpoint is the source node, that is, starting from the source node, and searching for the third network stream submap including the source node, then the second node may be the fifth network stream submap. a sink node; when the first endpoint is a sink node, that is, starting from the sink node, and searching for a third network stream submap including the sink node, the second node may become the fifth network stream A source node of the subgraph.

FIG. 4 is a schematic diagram of a first sub-picture according to an embodiment of the present invention. As shown in FIG. 3 and FIG. 4, after acquiring a network stream sub-picture of seven nodes including a junction point numbered 10 Obtaining nodes other than the nodes numbered 4, 5, 6, 7, 8, 9, and 10 in the network flow graph to be processed, that is, nodes numbered 0, 1, 2, and 3, and the number For the edges between the nodes of 0, 1, 2, and 3, remove the edges between the nodes numbered 0, 1, 2, and 3, and aggregate the nodes numbered 0, 1, 2, and 3 into one. Nodes, the nodes obtained by merging can be referred to as nodes numbered s*. Then, the network sub-picture and the second node obtained according to the search form a first sub-picture, and the first sub-picture includes the

nodes

4 and 5, 6, 7, 8, 9, 10 obtained by the search, and the number is s. * The node, and the edge between the nodes numbered 4, 5, 6, 7, 8, 9, 10, s*. The node numbered 10 is the first of the first subgraph End point, the node numbered s* is the second end point of the first sub-picture, and since the node numbered 10 is the network connection point to be processed, the node numbered 10 is the sink point of the first sub-picture. The node numbered s* is the source node of the first submap.

S204. The first minimum cut subgraph of the fifth network stream submap is used as the first network stream submap according to the minimum cut partition of the fifth network stream submap.

In this embodiment, the maximum flow of the fifth network stream submap may be calculated to obtain a maximum flow of the fifth network flow submap, and the maximum flow of the fifth network flow submap is equal to the minimum cut of the fifth network flow submap. Capacity, thereby obtaining a minimum cut set of the fifth network stream sub-picture, the capacity of the minimum cut set being equal to the maximum flow of the first sub-picture, and performing the fifth network flow sub-picture according to the minimum cut set of the first network flow sub-picture The minimum cut is obtained, and the minimum cut of the fifth network stream subgraph is obtained, that is, two mutually disconnected network stream subgraphs obtained by removing the minimum cut set in the fifth network stream subgraph, if a network stream subgraph includes the first The source node of the fifth network stream submap, then the other network stream subgraph includes the sink node of the fifth network stream submap, and at the same time, the two disconnected network stream subgraphs may be referred to as the first minimum cut graph. And a second minimum cut subgraph, therefore, the minimum cut of the fifth network stream submap includes a second minimum cut subgraph of the first minimum cut subgraph of the fifth network flow submap, and then the fifth network flow submap First minimum cut subgraph as the first network flow FIG., The first minimum cut subgraph comprises M nodes, M comprises a first end-node. Since the first network stream submap is a part of the fifth network stream submap, the preset number may be greater than or equal to M.

It should be noted that, how to perform the maximum stream calculation on the fifth network stream sub-picture, and obtain the minimum cut set of the fifth network stream sub-picture is consistent with the prior art, and details are not repeatedly described herein.

For example, as shown in FIG. 4, in the first sub-picture shown in FIG. 4, the maximum flow of the first sub-picture is 15, then the minimum cut capacity of the first sub-picture is 15, and the number is 4 and The capacity of the edge between the nodes numbered 7, the capacity of the edge between the node numbered 5 and the node numbered 8, the edge between the node numbered 9 and the node numbered 10 The capacity, the sum of 15, then the edge between the node numbered 4 and the node numbered 7, the edge between the node numbered 5 and the node numbered 8, the junction numbered 9 The edge between the point and the node numbered 10 can be collectively referred to as the minimum cut of the first subgraph, then the minimum cut set includes the node numbered 7, the node numbered 8 and the node numbered 10, or The minimum cut set includes a node numbered s*, a node numbered 4, a node numbered 5, a node numbered 6 and a node numbered 9. Therefore, according to the minimum cut set, the first sub-picture can be divided into a first minimum cut sub-picture and a second minimum cut sub-picture, and the first minimum cut sub-picture is a node numbered 7 and numbered 8 , the node numbered 10, And the edge composition between the nodes numbered 7, 8, 10, then the second minimum cut subgraph is a node numbered s*, a node numbered 4, a node numbered 5, numbered The node of 6, the node numbered 9, and the edge between the nodes numbered s*, 4, 5, 6, and 9.

S205. Combine the first network stream submap into a first node.

In this embodiment, the specific implementation process of S205 is similar to the specific implementation process of S202 in the first embodiment of the present invention. For details, refer to related descriptions in the foregoing embodiments, and details are not described herein again.

For example, FIG. 5 is a schematic diagram of a first sub-picture including a first node according to an embodiment of the present invention. As shown in FIG. 5, after obtaining the first minimum cut sub-picture, the first minimum cut sub-picture is represented by a number. For the 3 nodes of the sink node of 10 and the edge composition between the 3 nodes, the node numbered 7 in the first minimum cut graph, the node numbered 8 is numbered 10 The edge between the nodes is removed, and the node numbered 7, the node numbered 8, and the node numbered 10 are aggregated into a first node, which is the node numbered t*. .

S206. Restore the second node to a fourth network stream submap.

In this embodiment, the second node may be restored, that is, the second node is restored to a fourth network stream submap other than the third network stream submap in the to-be-processed network flow graph, that is, the second node. The node is restored to all nodes in the fourth network stream submap, and the edges between all the nodes in the fourth network stream submap are restored. And the edge between the second node and all the nodes of the third network stream sub-picture becomes the edge between all the nodes of the fourth network stream sub-picture and all the nodes of the third network stream sub-picture.

S207. The first network node and the second network stream sub-picture except the first network stream sub-picture in the to-be-processed network flow graph are combined into a first reduced network flow graph.

In this embodiment, the specific implementation process of S207 is similar to the specific implementation process of S103 in the first embodiment of the present invention. For details, refer to related descriptions in the foregoing embodiments, and details are not described herein again.

6 is a schematic diagram of a first reduced network flow diagram according to an embodiment of the present invention. As shown in FIG. 6, after obtaining a first node, that is, a node numbered t*, a node of s* is used. The restoration is performed, that is, the node of s* is restored to the node numbered 0, 1, 2, and 3, and the edge between the nodes numbered 0, 1, 2, and 3. Then the nodes numbered 0, 1, 2, 3, 4, 5, 6, 9, t*, and the nodes numbered 0, 1, 2, 3, 4, 5, 6, 9, t* The edges between the components constitute the first reduced network flow graph. The network flow graph reduction method provided by the embodiment of the present invention can reduce the to-be-processed network flow graph shown in FIG. 3 to the first reduced network flow graph shown in FIG. 6 , and the first reduced network. The flow graph is reduced by two nodes compared to the network flow graph to be processed, so that the scale of the graph is reduced. At the same time, the maximum flow of the to-be-processed network flow graph shown in FIG. 3 is 11, that is, the minimum cut capacity of the to-be-processed network flow graph is 11, and the minimum cut capacity is between the node numbered 0 and number 1. The capacity of the side, the capacity of the edge between the number 2 and the node numbered 5, the capacity of the edge between the number 5 and the node numbered 9, and the number 9 and the node numbered 10. The sum of the capacities of the sides. The maximum flow of the first reduced network flow graph shown in FIG. 6 is also 11, that is, the minimum cut capacity of the first reduced network flow graph is 11, and the minimum cut capacity is also the node numbered 0 and numbered 1. The capacity of the side, the capacity of the side between the number 2 and the node numbered 5, the capacity of the side between the number 5 and the node numbered 9, and the number 9 and the number 10 The sum of the capacities between the sides. Therefore, the maximum flow minimum cut of the to-be-processed network flow diagram shown in FIG. 3 is equal to the maximum flow minimum cut of the maximum flow minimum cut of the first reduced network flow diagram shown in FIG. 6, and the first reduced network flow diagram shown in FIG. Equivalent to the network flow graph to be processed shown in Figure 3.

The network flow graph reduction method provided by the second embodiment of the present invention, by searching from the first endpoint, searches for a third network stream submap including a preset number of nodes, and divides the third network stream in the to-be-processed network flow graph. The fourth network stream sub-picture outside the sub-picture is merged into a second node, and the second node and the third network stream sub-picture are combined into a fifth network stream sub-picture, according to the minimum cut of the fifth network stream sub-picture. The first minimum cut subgraph of the fifth network stream submap is used as the first network stream submap, the first network stream submap is merged into one first node, and the second node is restored to the fourth network stream. For example, the first node and the second network stream sub-picture other than the first network stream sub-picture in the to-be-processed network flow graph form a first reduced network flow graph. By merging the first network stream submap including the M nodes into the first node, the first node becomes the first endpoint of the reduced first reduced network flow graph, which can effectively reduce the scale of the graph. There is no need to process the network flow graph to meet certain rules, so that the process of reducing the scale of the graph has universal applicability.

FIG. 7 is a flowchart of Embodiment 3 of a network flow graph reduction method according to the present invention. As shown in FIG. 7 , the method in this embodiment may be based on the network flow graph reduction method embodiment shown in FIG. 1 or FIG. 2 . include:

S301. Record a reduced number of times of the network flow graph to be processed, and obtain a reduced number of times of the network flow graph to be processed.

In this embodiment, after the network flow graph to be processed is reduced, the number of times of reduction of the network flow graph to be processed is recorded, so that the total number of reductions of the network flow graph to be processed can be obtained. For example, the network flow graph to be processed before the network flow graph is to be processed for reduction. The number of reductions is recorded as 0. When the network flow graph to be processed is reduced, the number of reductions of the network flow graph to be processed is incremented by one, so that the number of reductions of the network flow graph to be processed after the reduction processing can be obtained.

S302. Determine whether the number of times of reduction of the to-be-processed network flow graph is less than the first preset number of times. If yes, execute S303. If no, execute S304.

In this embodiment, after obtaining the reduced number of times of the network flow graph to be processed, determining whether the number of times of reduction of the network flow graph to be processed is less than the first preset number of times, if it is smaller, it indicates that the network flow graph to be processed may be reduced. That is, S303 is executed. If it is not less than, it means that the network flow graph to be processed is not reduced, that is, S304 is executed. The first preset number of times may be the number of iterations set by the user, or may be the default number of iterations of the system. The first preset number of times may be determined according to an actual application scenario, which is not limited herein.

S303. Update the first reduced network flow graph to a network flow graph to be processed.

In this embodiment, if the number of times of reduction of the network flow graph to be processed is less than the first preset number of times, it indicates that the network flow graph to be processed may be reduced, and then the first reduced network flow graph is updated to the network flow graph to be processed. That is, S101-S103 is executed again or S201-S207 is executed again.

S304. End the process.

In this embodiment, if the number of times of reduction of the network flow graph to be processed is not less than the first preset number of times, it indicates that the network flow graph to be processed is not reduced, and then the process ends.

In the first feasible implementation manner, when the first endpoint is the source node, that is, the processing network flow graph is reduced from the source node of the to-be-processed network flow graph each time, that is, from the network stream to be processed. The source node of the graph begins to process the network flow graph for a first predetermined number of reductions.

In a second feasible implementation manner, when the first endpoint is a sink node, that is, each time the processing network flow graph is reduced from the sink point of the to-be-processed network flow graph, that is, the network flow to be processed is The sink point of the graph begins to process the network flow graph for a first predetermined number of reductions.

It should be noted that when the first preset number of times is set properly, the network flow graph to be processed can be reduced to two nodes, one node is the source node, and the other node is merged by the minimum cut subgraph. The resulting node, the new sink node, then the edge between the source node and the new sink node is the minimum cut set. Or, one node is a sink node, and the other node is a node merged by a minimum cut subgraph, that is, a new source node, then the edge between the new source node and the sink node is the smallest Cut the collection.

The network flow graph reduction method provided by the third embodiment of the present invention is further processed by The number of times of reduction of the network flow graph is recorded, and the number of times of the network flow graph to be processed is reduced. If the number of times of the network flow graph to be processed is less than the first preset number, the first reduced network flow graph is updated to the network flow graph to be processed. , then reduce the processing. This can effectively and greatly reduce the scale of the graph, and does not require the network flow graph to be processed to meet certain rules, so that the process of reducing the scale of the graph has universal applicability.

FIG. 8 is a flowchart of Embodiment 4 of a network flow graph reduction method according to the present invention. As shown in FIG. 8 , the method in this embodiment is based on any embodiment of the network flow graph reduction method shown in FIG. 1 to FIG. 3 . It can also include:

S401. Acquire a sixth network stream submap from the first reduced network flow graph.

The sixth network stream submap includes an edge between the K nodes and the K nodes, and K is an integer greater than or equal to 2. When the first endpoint is the source node, the second endpoint is the sink node. When the first endpoint is a sink node, the second endpoint is a source node.

S402. Combine the sixth network stream submap into a third node.

S403. The third node and the seventh network stream submap except the sixth network stream submap in the first reduced network flow graph form a second reduced network flow graph.

Wherein the seventh network stream submap is removed from all remaining nodes except the sixth network stream submap in the first reduced network flow graph and all remaining nodes except the sixth network stream submap Edge composition; the edge between all nodes of the sixth network stream subgraph and all nodes of the seventh network stream subgraph becomes the edge between all nodes of the third node and the seventh network stream subgraph, The second reduced network flow graph includes a seventh network stream submap, a third node, and an edge between all nodes of the third node and the seventh network stream submap, and the second reduced network flow graph is minimally cut. The capacity is equal to the minimum cut capacity of the network flow graph to be processed, and the third node is the second end point of the second reduced network flow graph.

The specific implementation process of S401-S403 in the embodiment of the present invention is similar to the specific implementation process of S101-S103 in the first embodiment of the present invention, or the specific implementation process of S401-S403 in the embodiment of the present invention and the method of the present invention The specific implementation process of the S201-S207 in the second embodiment is similar. For details, refer to the related description in the foregoing embodiment, and details are not described herein again.

In a feasible implementation manner, starting from a source node of the network flow graph to be processed, the network flow graph to be processed is subjected to a reduction process to obtain a first reduced network flow graph; and then the sink is reduced from the first network flow graph. At the beginning of the node, the first reduced network flow graph is subjected to a reduction process to obtain a second reduced network flow graph; and then the second reduced network flow graph is updated to the pending network flow graph, from the updated pending network flow graph. The source node starts, and the updated network flow graph to be processed Performing a reduction process to obtain a first reduced network flow graph; then, starting from the sink point of the first reduced network flow graph, performing a reduction process on the first reduced network flow graph to obtain a second reduced network flow graph; In this way, the reduction process is performed from the source node at a time, and the reduction process is started from the sink node at a time. Alternatively, starting from the sink point of the network flow graph to be processed, the network flow graph to be processed is subjected to a reduction process to obtain a first reduced network flow graph; and then starting from the source node of the first reduced network flow graph, the first The network flow graph is reduced to perform a reduction process to obtain a second reduced network flow graph; then the second reduced network flow graph is updated to be a pending network flow graph, starting from the sink point of the updated pending network flow graph, and updating The to-be-processed network flow graph is subjected to a reduction process to obtain a first reduced network flow graph; and then, starting from the source node of the first reduced network flow graph, the first reduced network flow graph is subjected to a reduction process to obtain the first Second, the network flow graph is reduced; and so on, the reduction processing is started from the sink node once, and the reduction processing is performed from the source node at a time. In the case that the number of times of reduction processing is appropriate, the network flow graph to be processed can be reduced to two nodes, and one node is a node formed by merging the smallest cut sub-pictures, that is, a new source node and another node. It is also the node that is merged by the smallest cut subgraph, that is, the new sink point, then the edge between the new source node and the new sink point is the minimum cut.

In another feasible implementation manner, the network flow graph to be processed may be reduced from the source node of the network flow graph to be processed, and when the number of times of the network flow graph to be processed is not less than the first preset number, The description may stop reducing the processing of the network flow graph from the source node, and then reduce the first reduced network flow graph from the sink point of the first reduced network flow graph obtained by the reduction processing. Alternatively, the network flow graph to be processed may be reduced from the sink point of the network flow graph to be processed, and when the number of times of the network flow graph to be processed is not less than the first preset number, the slave node may no longer be removed from the sink node. The processing of the network flow graph is started to be reduced, and then the first reduced network flow graph is reduced from the source node of the first reduced network flow graph obtained by the reduction processing.

The network flow graph reduction method provided by Embodiment 4 of the present invention further includes: obtaining a sixth network stream submap from the first reduced network flow graph; and merging the sixth network stream submap into a third node; The third node and the seventh network stream submap except the sixth network stream submap in the first reduced network flow graph form a second reduced network flow graph, and the minimum cut capacity of the second reduced network flow graph is equal to the network to be processed. The minimum cut capacity of the flow graph, and the third node is the second end point of the second reduced network flow graph. By merging the sixth network stream submap including K nodes into a third node, the third node becomes the second endpoint of the reduced second reduced network flow graph, which can effectively reduce the scale of the graph, The network flow graph to be processed needs to meet certain rules, so that the process of reducing the scale of the graph has universal applicability.

FIG. 9 is a flowchart of Embodiment 5 of a network flow graph reduction method according to the present invention. As shown in FIG. 9 , the method in this embodiment may further include:

S501. Record the reduced number of times of the first reduced network flow graph, and obtain the reduced number of times of the first reduced network flow graph.

In this embodiment, each time the first reduced network flow graph is reduced, the number of times of reduction of the first reduced network flow graph is recorded, so that the total number of reductions of the first reduced network flow graph can be obtained. For example, before the first reduced network flow graph is reduced, the number of reductions of the first reduced network flow graph is recorded as 0, and when the first reduced network flow graph is reduced, the first reduced network flow graph is obtained. The number of reductions is incremented by one, so that the number of reductions of the first reduced network flow graph after this reduction process can be obtained.

S502. Determine whether the number of times of reduction of the first reduced network flow graph is less than a second preset number. If yes, execute S503. If no, execute S504.

In this embodiment, after obtaining the reduced number of times of the first reduced network flow graph, determining whether the number of times of reduction of the first reduced network flow graph is less than a second preset number of times, and if less than, indicating that the first reduced network flow graph is further The reduction processing is performed, that is, S503 is executed. If it is not smaller, it means that the first reduced network flow graph can no longer be reduced, that is, S504 is executed. The second preset number of times may be the number of iterations set by the user, and may be the default number of iterations of the system. The second preset number of times may be determined according to an actual application scenario, which is not limited herein.

S503. Update the second reduced network flow graph to the first reduced network flow graph.

In this embodiment, if the number of times of reduction of the first reduced network flow graph is less than the second preset number of times, it may be further that the first reduced network flow graph may be reduced, and then the second reduced network flow graph is updated to the first reduced The network flow graph, that is, S401-S403 is executed again.

S504, ending the process.

In this embodiment, if the number of times of reduction of the first reduced network flow graph is not less than the second preset number of times, it may be that the first reduced network flow graph may not be reduced, and then the process ends.

In the first feasible implementation manner, the network flow graph to be processed may be reduced from the source node of the network flow graph to be processed, and when the number of times of the network flow graph to be processed is not less than the first preset number, The description can no longer reduce the processing of the network flow graph from the source node. Then, starting from the sink point of the first reduced network flow graph obtained by the reduction process, the first reduced network flow graph is reduced, and when the number of reductions of the first reduced network flow graph is not less than the second preset number, The processing of the network flow graph is no longer reduced from the sink node, that is, the reduction processing is completed, and the flow is ended. Alternatively, the network flow graph to be processed may be reduced from the sink point of the network flow graph to be processed, and when the number of times of the network flow graph to be processed is not less than the first preset number, the description may no longer be from the sink node. Start to process the network flow graph for reduction processing, and then reduce the first reduced network flow graph from the source node of the first reduced network flow graph obtained by the reduction processing, when the first reduced network flow graph is reduced by a small number of times If the second preset number is less than the second preset number, it may be that the network flow graph to be processed is not reduced from the source node, that is, the reduction processing is completed, and the flow is ended. In the case that the number of times of reduction processing is appropriate, the network flow graph to be processed can be reduced to two nodes, and the two nodes are respectively nodes merged by different minimum cut sub-graphs, that is, new source nodes and The new sink point, then the edge between the new source node and the new sink node is the minimum cut set.

In a second feasible implementation manner, the network flow graph to be processed may be reduced from the source node of the network flow graph to be processed, and then the sink point of the first reduced network flow graph obtained by the reduction processing is started. The reduction of the first reduced network flow graph is performed. When the number of reductions of the first reduced network flow graph is not less than the second preset number of times, it indicates that the network flow graph to be processed may not be reduced from the sink node, that is, completed. Reduce processing and end the process. Alternatively, the network flow graph to be processed may be reduced from the sink point of the network flow graph to be processed, and then the first reduced network flow graph is started from the source node of the first reduced network flow graph obtained by the reduction processing. The reduction processing, when the number of reductions of the first reduced network flow graph is not less than the second preset number of times, indicates that the network flow graph to be processed may not be reduced from the source node, that is, the reduction processing is completed, and the flow is ended.

The network flow graph reduction method provided by the fifth embodiment of the present invention further obtains the reduced number of times of the first reduced network flow graph by recording the reduced number of times of the first reduced network flow graph; when the first reduced network flow graph is reduced When the number of times is less than the second preset number of times, the second reduced network flow graph is updated to the first reduced network flow graph, and then the reduction processing is performed. This can effectively and greatly reduce the scale of the graph, and does not require the network flow graph to be processed to meet certain rules, so that the process of reducing the scale of the graph has universal applicability.

FIG. 10 is a schematic structural diagram of Embodiment 1 of a network flow graph reduction apparatus according to the present invention. As shown in FIG. 10, the apparatus in this embodiment may include: an obtaining unit 11, a merging unit 12, and a processing unit 13, The obtaining unit 11 is configured to obtain a first network stream submap from the to-be-processed network flow graph, where the first network stream submap includes edges between the M nodes and the M nodes, and the M nodes The point includes a first endpoint, the M is an integer greater than or equal to 2, and the to-be-processed network flow graph includes an edge between the N nodes and the N nodes, where the N nodes include a source a node and a sink node, where N is an integer greater than M, the first endpoint is a source node or a sink node, and the source node is a network flow used to represent the to-be-processed network flow graph The starting node, the sink node is an end node of the network flow, wherein an edge between each node represents a network flow relationship between the nodes; a merging unit 12 is configured to acquire the unit 11 The acquired first network stream sub-graphs are merged into one first node; the processing unit 13 is configured to merge the first nodes obtained by combining the merging unit 12 with the first network stream sub-picture in the to-be-processed network flow graph. a second network stream submap other than the first network flow graph, the second network stream submap being divided by the to-be-processed network flow graph All remaining nodes outside the first network stream sub-picture and edges between the remaining nodes; all nodes of the first network stream sub-picture and the second network stream sub-picture An edge between all nodes becomes an edge between the first node and all nodes of the second network stream submap, the first reduced network flow graph including the first node, the a second network stream submap, and an edge between the first node and all nodes of the second network stream submap, the minimum cut capacity of the first reduced network flow graph is equal to the to-be-processed The minimum cut capacity of the network flow graph, the first node being the first endpoint of the first reduced network flow graph.

The device in this embodiment may be used to perform the technical solution of the foregoing method embodiment of the present invention. The implementation principle and the technical effect are similar. For details, refer to related descriptions in the foregoing embodiments of the present invention, and details are not described herein again.

FIG. 11 is a schematic structural diagram of Embodiment 2 of a network flow graph reduction device according to the present invention. As shown in FIG. 11 , the device in this embodiment is based on the device structure shown in FIG. 10 , and optionally, the merging unit 12 is specifically configured to An edge between the M nodes of the first network stream submap is removed, and the M nodes are aggregated into one of the first nodes.

Optionally, the obtaining unit 11 is specifically configured to: start from the first endpoint, search for a third network stream submap including a preset number of nodes, where the third network stream submap includes the search An edge between the preset number of nodes and the preset number of nodes obtained by the search, the preset number is greater than or equal to the M; and the network flow graph to be processed is divided The fourth network stream submap outside the third network stream submap is merged into a second node, and the fourth network stream submap is removed from the to-be-processed network flow graph by the third network stream All remaining nodes outside the graph and Determining an edge composition between all remaining nodes except the third network stream submap; and forming the second node and the third network stream submap into a fifth network stream submap, An edge between all nodes of the fourth network stream submap and all nodes of the third network stream submap becomes between the second node and all nodes of the third network stream submap The fifth network stream submap includes the second node, the third network stream submap, and all nodes between the second node and the third network stream submap The second node is a second endpoint of the fifth network stream submap; wherein, when the first endpoint is a source node, the second endpoint is a sink node, when When the first endpoint is a sink node, the second endpoint is a source node; according to the minimum cut partition of the fifth network stream submap, the first minimum cut graph of the fifth network stream submap is As the first network stream submap.

Optionally, the apparatus in this embodiment may further include: a restoring unit 14 configured to obtain, according to a minimum cut partition of the fifth network stream submap, the fifth network stream submap. After the minimum cut subgraph is used as the first network stream submap, the second node is restored to the fourth network stream submap, and the second node and the third network stream submap are The edge between all nodes becomes the edge between all nodes of the fourth network stream submap and all nodes of the third network stream submap.

Optionally, the apparatus in this embodiment may further include: a first recording unit 15 configured by the processing unit 13 to divide the first node and the to-be-processed network flow diagram except the first network After the second network stream submap other than the stream submap constitutes the first reduced network flow graph, the number of times of the to-be-processed network flow graph is reduced, and the number of times of the to-be-processed network flow graph is obtained.

Optionally, the apparatus of this embodiment may further include: a first updating unit 16, where the first update unit 16 is configured to reduce the number of times of the to-be-processed network flow graph obtained by the first recording unit 15 to be less than the first pre- And setting the number of times, updating the first reduced network flow graph to the to-be-processed network flow graph.

FIG. 12 is a schematic structural diagram of Embodiment 3 of a network flow graph reduction apparatus according to the present invention. As shown in FIG. 12, the apparatus of this embodiment is based on the apparatus structure shown in FIG. 11, and further, if the first recording unit 15 records and obtains The obtaining unit 11 is further configured to obtain the sixth network stream submap from the first reduced network flow graph, where the number of times of the to-be-processed network flow graph is not smaller than the first preset number of times. The sixth network stream submap includes edges between K nodes and K nodes, the K is an integer greater than or equal to 2, and the K nodes include a second endpoint, where When the first endpoint is a source node, the second endpoint is a sink node, and when the first endpoint is a sink node, the second endpoint is a source node; the merging unit 12 is further used Combining the sixth network stream sub-graph obtained by the obtaining unit 11 into a third node; the processing unit 13 is further configured to merge the third node obtained by the merging unit 12 with the first reduction The seventh network stream submap in addition to the sixth network stream submap in the network flow graph constitutes a second reduced network flow graph, wherein the seventh network stream submap is removed from the first reduced network flow graph All remaining nodes other than the six network stream sub-pictures and the edges between the remaining nodes except the sixth network stream sub-picture are deleted; all nodes of the sixth network stream sub-picture are An edge between all nodes of the seventh network stream submap becomes all nodes of the third node and the seventh network stream submap The second reduced network flow graph includes the seventh network stream submap, the third node, and all nodes of the third node and the seventh network stream submap An edge between the second reduced network flow graph having a minimum cut capacity equal to a minimum cut capacity of the to-be-processed network flow graph, the third node being a second of the second reduced network flow graph End point.

Optionally, the apparatus of this embodiment may further include: a second recording unit 17, configured by the processing unit 13 to divide the third node from the first reduced network flow graph After the seventh network stream submap other than the six network stream submaps constitutes the second reduced network flow graph, the number of reductions of the first reduced network flow graph is recorded, and the number of reductions of the first reduced network flow graph is obtained. .

Optionally, the apparatus of this embodiment may further include: a second update unit 18, where the second update unit 18 is configured to reduce the number of times of the first reduced network flow graph obtained by the second recording unit 17 to be smaller than And a second preset number of times, updating the second reduced network flow graph to the first reduced network flow graph.

FIG. 13 is a schematic structural diagram of Embodiment 4 of a network flow graph reduction apparatus according to the present invention. As shown in FIG. 13, the apparatus of this embodiment includes a memory 21 and a processor 22 connected to the memory 21, wherein the memory 21 stores a set of programs. The code 21 may include a non-volatile memory. The processor 22 can be a central processor (Central) A processing unit (CPU), or an Application Specific Integrated Circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of the present invention. The processor 22 is configured to call the program code stored in the memory 21 for performing the following operations:

Acquiring a first network stream sub-picture from the to-be-processed network flow graph, where the first network stream sub-picture includes an edge between the M nodes and the M nodes, where the M nodes include the first end point The M is an integer greater than or equal to 2, and the to-be-processed network flow graph includes an edge between the N nodes and the N nodes, where the N nodes include a source node and a sink node. The N is an integer greater than M, the first endpoint is a source node or a sink node, and the source node is a starting node of a network flow used to represent the to-be-processed network flow graph. The summary node is an end node of the network flow, wherein an edge between each node represents a network flow relationship between the nodes;

Combining the first network stream submap into a first node;

Optionally, the merging the first part of the to-be-processed network flow graph into a first node comprises: removing an edge between the M nodes of the first network stream submap; The nodes are aggregated into one of the first nodes.

Optionally, the obtaining the first network stream submap from the to-be-processed network flow graph includes:

Starting from the first endpoint, searching for a third network stream submap including a preset number of nodes, where the third network stream submap includes the preset number of nodes and locations obtained by the search The search for the edge between the preset number of nodes, the preset number is greater than or equal to the M;

Merging the fourth network stream submap other than the third network stream submap in the to-be-processed network flow graph into a second node, where the fourth network stream submap is used by the to-be-processed network stream Removing all remaining nodes except the third network stream submap and removing the third network stream The edge between all remaining nodes outside the subgraph;

Optionally, after the first minimum cut sub-picture of the fifth network stream sub-picture is used as the first network stream sub-picture according to the minimum cut partition of the fifth network stream sub-map, the method further includes:

Optionally, after the first node and the second network stream submap other than the first network stream submap in the to-be-processed network flow graph are formed into the first reduced network flow graph, the method further includes: Recording the reduced number of times of the to-be-processed network flow graph to obtain a reduced number of times of the to-be-processed network flow graph.

Optionally, if the number of times of reduction of the to-be-processed network flow graph is less than the first preset number of times, updating the first reduced network flow graph to the to-be-processed network flow graph.

Optionally, if the number of times of the network flow graph to be processed is not less than the first preset number of times, the method further includes:

Combining the sixth network stream submap into a third node;

Forming, by the third node, a seventh network stream sub-picture other than the sixth network stream sub-picture in the first reduced network flow graph to form a second reduced network flow graph, where the seventh network flow sub-graph is configured by The first Reducing, in the network flow graph, all remaining nodes except the sixth network stream submap and edge components between the remaining nodes except the sixth network stream submap; An edge between all nodes of the network stream submap and all nodes of the seventh network stream submap becomes an edge between the third node and all nodes of the seventh network stream submap The second reduced network flow graph includes the seventh network stream submap, the third node, and an edge between the third node and all nodes of the seventh network stream submap The minimum cut capacity of the second reduced network flow graph is equal to the minimum cut capacity of the first reduced network flow graph, and the third node is the second endpoint of the second reduced network flow graph.

Optionally, after the third node and the seventh network stream submap other than the sixth network stream submap in the first reduced network flow graph form a second reduced network flow graph, the method further includes : recording the reduced number of times of the first reduced network flow graph to obtain a reduced number of times of the first reduced network flow graph.

Optionally, if the number of times of reduction of the first reduced network flow graph is less than a second preset number of times, updating the second reduced network flow graph to the first reduced network flow graph.

It should be noted that the technical solution that the processor 22 specifically implements by calling the program code stored in the memory 21 can refer to the foregoing embodiment of the network flow graph reduction method of the present invention. The implementation principle and technical effects are similar. For details, refer to the foregoing embodiment. The relevant records in the description are not repeated here.

One of ordinary skill in the art will appreciate that all or part of the steps to implement the various method embodiments described above may be accomplished by hardware associated with the program instructions. The aforementioned program can be stored in a computer readable storage medium. The program, when executed, performs the steps including the foregoing method embodiments; and the foregoing storage medium includes various media that can store program codes, such as a ROM, a RAM, a magnetic disk, or an optical disk.

Finally, it should be noted that the above embodiments are merely illustrative of the technical solutions of the present invention, and are not intended to be limiting; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art will understand that The technical solutions described in the foregoing embodiments may be modified, or some or all of the technical features may be equivalently replaced; and the modifications or substitutions do not deviate from the technical solutions of the embodiments of the present invention. range.

Claims

A network flow graph reduction method, comprising:

Acquiring a first network stream sub-picture from the to-be-processed network flow graph, where the first network stream sub-picture includes an edge between the M nodes and the M nodes, where the M nodes include the first end point The M is an integer greater than or equal to 2, and the to-be-processed network flow graph includes an edge between the N nodes and the N nodes, where the N nodes include a source node and a sink node. The N is an integer greater than M, the first endpoint is a source node or a sink node, and the source node is a starting node of a network flow used to represent the to-be-processed network flow graph. The summary node is an end node of the network flow, wherein an edge between each node represents a network flow relationship between the nodes;

Combining the first network stream submap into a first node;

Forming, by the first node, a second network stream submap other than the first network stream submap in the to-be-processed network flow graph to form a first reduced network flow graph, where the second network proxy submap is Determining, in the processing network flow graph, all remaining nodes except the first network stream submap and edge components between the remaining nodes; all nodes and locations of the first network stream submap An edge between all nodes of the second network stream submap becomes an edge between the first node and all nodes of the second network stream submap, and the first reduced network flow graph includes a first node, the second network stream submap, and an edge between the first node and all nodes of the second network stream submap, the minimum of the first reduced network flow graph The cut capacity is equal to the minimum cut capacity of the to-be-processed network flow graph, and the first node is the first endpoint of the first reduced network flow graph.
The method according to claim 1, wherein the merging the first part of the to-be-processed network flow graph into a first node comprises:

Removing the edge between the M nodes of the first network stream submap;

The M nodes are aggregated into one of the first nodes.
The method according to claim 1 or 2, wherein the obtaining the first network stream submap from the to-be-processed network flow graph comprises:

Starting from the first endpoint, searching for a third network stream submap including a preset number of nodes, where the third network stream submap includes the preset number of nodes and locations obtained by the search The search for the edge between the preset number of nodes, the preset number is greater than or equal to the M;

Merging the fourth network stream submap other than the third network stream submap in the to-be-processed network flow graph into a second node, where the fourth network stream submap is used by the to-be-processed network stream In addition to the figure Determining an edge between all remaining nodes except the third network stream submap and all remaining nodes except the third network stream submap;

Forming, by the second node and the third network stream submap, a fifth network stream submap, where all nodes of the fourth network stream submap and all nodes of the third network stream submap An edge between the second node and all nodes of the third network stream submap, the fifth network stream submap including the second node, the third network a stream submap and an edge between the second node and all nodes of the third network stream submap, the second node being a second endpoint of the fifth network stream submap;

Wherein, when the first endpoint is a source node, the second endpoint is a sink node, and when the first endpoint is a sink node, the second endpoint is a source node;

And determining, according to the minimum cut partition of the fifth network stream submap, the first minimum cut subgraph of the fifth network stream submap as the first network stream submap.
The method according to claim 3, wherein the first minimum cut subgraph of the fifth network stream submap is used as the first according to a minimum cut partition of the fifth network stream submap After the network stream submap, it also includes:

Restoring the second node to the fourth network stream submap, and the edge between the second node and all nodes of the third network stream submap becomes the fourth network stream submap The edge between all nodes and all nodes of the third network stream submap.
The method according to any one of claims 1 to 4, wherein the first node and the second network stream except the first network stream submap in the to-be-processed network flow graph After the subgraph constitutes the first reduced network flow graph, it also includes:

Recording the reduced number of times of the to-be-processed network flow graph to obtain a reduced number of times of the to-be-processed network flow graph.
The method according to claim 5, wherein if the number of times of reduction of the to-be-processed network flow graph is less than a first preset number of times, updating the first reduced network flow graph to the to-be-processed network flow graph .
The method according to claim 6, wherein the method further comprises: if the number of times of the network flow graph to be processed is not less than the first predetermined number of times, the method further comprises:

Obtaining a sixth network stream submap from the first reduced network flow graph, where the sixth network stream submap includes edges between K nodes and K nodes, where K is greater than or equal to 2 An integer, wherein the K nodes include a second endpoint, wherein when the first endpoint is a source node, the The second endpoint is a sink node, and when the first endpoint is a sink node, the second endpoint is a source node;

Combining the sixth network stream submap into a third node;

Forming, by the third node, a seventh network stream sub-picture other than the sixth network stream sub-picture in the first reduced network flow graph to form a second reduced network flow graph, where the seventh network flow sub-graph is configured by Removing, in the first reduced network flow diagram, all remaining nodes except the sixth network stream submap and edge components between the remaining nodes except the sixth network stream submap; An edge between all nodes of the sixth network stream submap and all nodes of the seventh network stream submap becomes all nodes of the third node and the seventh network stream submap The second reduced network flow graph includes the seventh network stream submap, the third node, and all nodes of the third node and the seventh network stream submap Between the edges, the minimum cut capacity of the second reduced network flow graph is equal to the minimum cut capacity of the first reduced network flow graph, and the third node is the second reduced network flow graph Two endpoints.
The method according to claim 7, wherein the third node and the seventh network stream submap other than the sixth network stream submap in the first reduced network flow graph are combined After reducing the network flow graph, it also includes:

Recording the number of reductions of the first reduced network flow graph to obtain a reduced number of times of the first reduced network flow graph.
The method according to claim 8, wherein the second reduced network flow graph is updated to the first reduced network if the number of reductions of the first reduced network flow graph is less than a second predetermined number of times Flow chart.
A network flow graph reduction device, comprising:

An acquiring unit, configured to obtain a first network stream sub-picture from a to-be-processed network flow graph, where the first network stream sub-picture includes an edge between the M nodes and the M nodes, where the M nodes are Including a first endpoint, the M is an integer greater than or equal to 2, the to-be-processed network flow graph includes edges between N nodes and N nodes, and the N nodes include source nodes And a sink node, where N is an integer greater than M, the first endpoint is a source node or a sink node, and the source node is a network flow used to represent the to-be-processed network flow graph a start node, where the sink node is an end node of the network flow, wherein an edge between each node represents a network flow relationship between the nodes;

a merging unit, configured to merge the first network stream sub-graph obtained by the acquiring unit into a first node;

a processing unit, configured to merge the merged unit to obtain the first node and the to-be-before The second network stream submap in addition to the first network stream submap in the network flow graph constitutes a first reduced network flow graph, and the second network stream submap is removed from the to-be-processed network flow graph All remaining nodes except a network stream sub-picture and edges between the remaining nodes; all nodes of the first network stream sub-picture and all nodes of the second network stream sub-picture An edge between the first node and all nodes of the second network stream submap, the first reduced network flow graph including the first node, the second network a stream map, and an edge between the first node and all nodes of the second network stream submap, the minimum cut capacity of the first reduced network flow graph is equal to the to-be-processed network flow graph The minimum cut capacity, the first node being the first endpoint of the first reduced network flow graph.
The apparatus according to claim 10, wherein the merging unit is specifically configured to remove an edge between the M nodes of the first network stream submap and aggregate the M nodes into One of the first nodes.
The apparatus according to claim 10 or 11, wherein the obtaining unit is specifically configured to: start from the first endpoint, search for a third network stream submap including a preset number of nodes, The third network stream submap includes an edge between the preset number of nodes acquired by the search and the preset number of nodes acquired by the search, where the preset number is greater than or equal to the edge Merging a fourth network stream submap other than the third network stream submap in the to-be-processed network flow graph into a second node, where the fourth network stream submap is to be processed Removing, in the network flow graph, all remaining nodes except the third network stream submap and edge components between the remaining nodes except the third network stream submap; and The second node and the third network stream submap constitute a fifth network stream submap, and an edge between all nodes of the fourth network stream submap and all nodes of the third network stream submap, An edge between the second node and all nodes of the third network stream submap, the fifth network stream Include the second node, the third network stream submap, and an edge between the second node and all nodes of the third network stream submap, the second node being the a second endpoint of the fifth network flow submap; wherein, when the first endpoint is a source node, the second endpoint is a sink node, and when the first endpoint is a sink node, The second endpoint is a source node; according to the minimum cut partition of the fifth network stream submap, the first minimum cut subgraph of the fifth network stream submap is used as the first network stream submap.
The device according to claim 12, further comprising:

a restoring unit, configured to: after the obtaining, the first minimum cut sub-graph of the fifth network stream submap as the first network stream submap according to the minimum cut partition of the fifth network stream submap Restoring the second node to the fourth network stream submap, and the edge between the second node and all nodes of the third network stream submap becomes the fourth network stream submap The edge between all nodes and all nodes of the third network stream submap.
The device according to any one of claims 10-13, further comprising:

a first recording unit, configured by the processing unit to form, by the first node, a second network stream submap other than the first network stream submap in the to-be-processed network flow graph to form a first reduced network flow graph Then, the number of times of reduction of the to-be-processed network flow graph is recorded, and the number of times of reduction of the to-be-processed network flow graph is obtained.
The device according to claim 14, further comprising:

a first updating unit, configured to update the first reduced network flow graph to the to-be-processed if the number of times of reduction of the to-be-processed network flow graph obtained by the first recording unit is less than a first preset number of times Network flow diagram.
The apparatus according to claim 15, wherein the obtaining unit is further used if the number of times of reduction of the to-be-processed network flow graph obtained by the first recording unit is not less than a first preset number of times Obtaining a sixth network stream submap from the first reduced network flow graph, where the sixth network stream submap includes edges between K nodes and K nodes, where K is greater than or equal to 2 An integer, wherein the K nodes include a second endpoint, wherein when the first endpoint is a source node, the second endpoint is a sink node, and when the first endpoint is a sink node The second endpoint is a source node;

The merging unit is further configured to merge the sixth network stream submap obtained by the acquiring unit into a third node;

The processing unit is further configured to combine the third node obtained by combining the merging unit with a seventh network stream submap other than the sixth network stream submap in the first reduced network flow graph. Diluting a network flow graph, wherein the seventh network stream submap removes all remaining nodes except the sixth network stream submap from the first reduced network flow graph and the removing the sixth network stream a side between all remaining nodes except the sub-picture; the edge between all the nodes of the sixth network stream sub-picture and all the nodes of the seventh network stream sub-picture becomes the third An edge between the node and all nodes of the seventh network stream submap, the second reduced network flow graph including the seventh network stream submap, the third node, and the third An edge between the node and all nodes of the seventh network stream submap, and a minimum cut capacity of the second reduced network flow graph is equal to a minimum cut capacity of the to-be-processed network flow graph, the first The third node is the second endpoint of the second reduced network flow graph.
The device according to claim 16, further comprising:

a second recording unit, configured by the processing unit to form the third node and the seventh network stream submap other than the sixth network stream submap in the first reduced network flow graph to form a second reduced network stream After the figure, the number of reductions of the first reduced network flow graph is recorded, and the number of reductions of the first reduced network flow graph is obtained.
The device according to claim 17, further comprising:

a second updating unit, configured to update the second reduced network flow graph to the first if the number of times of reduction of the first reduced network flow graph obtained by the second recording unit record is less than a second preset number of times A reduced network flow graph.