JP2006180126A - Device and program for dividing network - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To suppress traffic intensity between network groups while considering spatial unities by groups obtained by dividing a network. <P>SOLUTION: A network information input means 11 inputs network information regarding the network to be divided to a network dividing device 10, a maximum tree extracting means 12 extracts the maximum tree of the network from the network information, and a base calculating means 13 calculates the base of a cocycle space belonging to the network from an edge of the maximum tree. A cassette calculating means 14 combines bases so that the traffic intensity between the divided networks does not exceed a threshold to calculate a cut set dividing the network. A convex function calculating means 15 calculates a convex function which is an evaluation function of subsets of nodes generated from the cut set and sorts cut sets by inter-class dispersion of the divided network. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a network partitioning apparatus and a network partitioning program, and is particularly suitable for application to a method of partitioning a network so that nodes constituting the network are spatially arranged.

When the network becomes enormous, the network is divided and managed from the viewpoint of network capacity and security. Here, in the conventional network partitioning method, since the management cost increases when the amount of traffic flowing between groups obtained by network partitioning is large, graph partitioning that performs partitioning that minimizes the amount of traffic flowing between groups Techniques that drop the problem are often used. For example, Non-Patent Document 1 discloses a technique for dividing a network by solving a genetic algorithm. Non-Patent Document 2 discloses a technique for solving a graph partitioning problem when the size of a group is limited.
Nozaki, Kawai “Performance Evaluation of Network Partitioning Method in WACNet”, IEICE General Conference B-7-49, 1993-3 B. W. Kernighan “An Effective Heuristic Procedure for Partitioning Graph”, Bell System Technical Journal, vol. 49, pp 291-307, 1970

However, with the conventional network partitioning method, the amount of traffic flowing between the groups obtained by network partitioning can be kept small, but the network is partitioned so that spatially distant nodes belong to the same group. There is a problem that the management cost may increase.
Accordingly, an object of the present invention is to provide a network partitioning device and a network partitioning program that can suppress the amount of traffic flowing between groups while considering a spatial unit for each group.

  In order to solve the above-described problem, according to the network dividing device according to claim 1, the division candidate extracting unit that extracts the network division candidates based on the traffic amount flowing between the divided networks; Node placement evaluation means for evaluating the spatial placement of nodes constituting the network with respect to the network division candidates extracted by the division candidate extraction means.

  As a result, it is possible to evaluate the spatial arrangement of the nodes constituting the network after extracting network division candidates so that the amount of traffic flowing between the divided networks is reduced. For this reason, it is possible to reduce the amount of traffic flowing between the divided networks while considering the spatial arrangement of the nodes, and the network management cost can be reduced.

  Also, according to the network partitioning device according to claim 2, the partition candidate extraction means inputs network information input for inputting information relating to a connection relationship between nodes constituting the network and an amount of traffic flowing through each edge between the nodes. A maximum tree extracting means for extracting a maximal tree of the network based on a connection relation between the nodes; a basis calculating means for calculating a base of a cocycle space belonging to the network from an edge of the maximal tree; Cutset calculation means for calculating a cutset for dividing the network by combining the bases so that the traffic volume does not exceed a threshold value, and the node placement evaluation means is calculated by the cutset calculation means Convex function that is an evaluation function of a subset of nodes created from a cutset Characterized in that it comprises a convex function calculating means for calculating.

  As a result, by combining the bases, it becomes possible to obtain all cut sets that divide the network, and it is possible to extract the network division candidates whose traffic volume does not exceed the threshold without omission. For this reason, it becomes possible to evaluate the spatial arrangement of nodes for all network division candidates whose traffic volume does not exceed the threshold, and the division candidates for which the spatial arrangement of nodes is evaluated. It is possible to reduce the amount of calculation of the convex function, and network partition candidates whose traffic volume does not exceed the threshold value spill from the evaluation target of the spatial arrangement of the nodes. Therefore, it is possible to efficiently divide the network while suppressing deterioration in the accuracy of dividing the network.

In addition, since it is possible to obtain the base by extracting a cut set that includes only one edge of the maximal tree, the amount of calculation necessary to obtain the base can be obtained by extracting the maximal tree of the network. The increase can be suppressed and pruning can be efficiently performed.
According to another aspect of the network dividing apparatus of the present invention, the maximal tree extracting means includes maximal tree selecting means for selecting a maximal tree having the maximum total amount of edge traffic among the maximal trees of the network. It is characterized by that.

  This makes it possible to increase the amount of traffic at the edge of a maximal tree, and when obtaining cut sets by sequentially combining bases, the edge of a maximal tree with a large amount of traffic can be incorporated into the cut set at an earlier stage. It becomes possible. For this reason, when the number of combinations of bases is smaller, a cut set whose traffic amount exceeds the threshold can be obtained, and subsequent base combinations for obtaining the cut set can be made unnecessary. As a result, it is possible to reduce the amount of calculation for obtaining network division candidates without leaking network division candidates whose traffic volume does not exceed the threshold, while suppressing deterioration in network division accuracy, The network can be divided efficiently.

Further, according to the network dividing apparatus according to claim 4, the cut set calculation means combines the bases based on at least one of the size of the traffic amount of the edge of the maximal tree and the number of edges of the base. A combination order setting means for setting the order is provided.
Here, by setting the order of combining the bases based on the traffic amount of the edge of the maximal tree, the edge of the maximal tree having a large traffic amount can be incorporated into the cut set at an earlier stage. For this reason, it is possible to obtain a cut set in which the traffic volume exceeds the threshold and the traffic volume does not fall below the threshold due to a symmetric difference from the subsequent bases when the number of base combinations is smaller. It is possible to eliminate the combination of the subsequent bases when obtaining. As a result, it is possible to reduce the amount of calculation for obtaining network division candidates without leaking network division candidates whose traffic volume does not exceed the threshold, while suppressing deterioration in network division accuracy, The network can be divided efficiently.

  Also, by setting the order of combining the bases based on the number of edges of the bases, it is possible to reduce sub-edges that may be combined at an earlier stage, and at a stage where the number of base combinations is smaller, It is possible to reduce the number of sub-edges that can be erased due to the difference in the basis symmetry. For this reason, when a cut set whose traffic volume exceeds the threshold value is obtained, a cut set in which the traffic volume does not fall below the threshold value regardless of the combination of the subsequent bases is obtained at a stage where the number of base combinations is smaller. Thus, it is possible to eliminate the combination of subsequent bases when obtaining a cut set. As a result, it is possible to reduce the amount of calculation for obtaining network division candidates while covering the network division candidates whose traffic volume does not exceed the threshold value, while suppressing deterioration in network division accuracy, The network can be divided efficiently.

  Further, according to the network dividing apparatus according to claim 5, the cut set calculation means includes a tree generation means for generating a tree representing all combinations of the bases according to an order of combining the bases, and a maximum of the combined bases. Pruning means for pruning the tree based on the total amount of traffic at the edge of the tree is provided.

  This makes it possible to incorporate the edge of a maximal tree with a large amount of traffic into the cut set at an earlier stage while covering all the combinations of the basis, and the traffic amount is set to a threshold value at a stage where the number of combinations of the basis is smaller. In addition, a cut set in which the traffic amount does not fall below a threshold value can be obtained from the difference in the basis symmetry thereafter. For this reason, when obtaining a cut set whose traffic volume does not exceed the threshold, it is possible to eliminate the combination of pruned bases without leaking a cut set whose traffic volume does not exceed the threshold. In addition, it is possible to prevent a network division candidate whose traffic volume does not exceed the threshold from falling out of the evaluation target of the spatial arrangement of the nodes, while suppressing degradation of the network division accuracy. Can be efficiently divided.

Further, according to the network dividing device according to claim 6, when the pruning means combines the bases according to the order of combining the bases, the total traffic amount of the edges of the maximal tree possessed by the combined bases exceeds a threshold value. In this case, a combination of bases lower than the base is omitted.
As a result, pruning can be performed based on the total traffic amount of the edges of the maximal tree that the combined base has, and the time required to obtain a cut set that does not exceed the threshold is reduced. be able to.

  Further, according to the network dividing apparatus according to claim 7, the cut set calculation means includes a tree generation means for generating a tree that expresses all combinations of the bases according to an order of combining the bases, and all the combined bases have And pruning means for pruning the tree based on the presence or absence of sub-edges or the traffic amount of the bases combined thereafter, and the traffic amount of the edges.

  This makes it possible to reduce all possible combinations of sub-edges at an earlier stage while covering all combinations of bases, and cut sets whose traffic volume exceeds the threshold when there are fewer base combinations. Can be requested. For this reason, it is possible to eliminate the subsequent combination of bases when obtaining a cut set, and network partition candidates whose traffic volume does not exceed the threshold are evaluated for the spatial arrangement of nodes. It is possible to prevent spilling from the network, and it is possible to efficiently divide the network while suppressing deterioration in the accuracy of dividing the network.

Further, according to the network dividing apparatus according to claim 8, when the pruning means combines the bases according to the order in which the bases are combined, the total traffic amount of all edges of the combined bases is calculated thereafter. If the threshold value is exceeded even if the traffic amount of the sub-edge that may be erased due to a symmetric difference from the combined base is exceeded, the combination of bases lower than that base is omitted.
As a result, pruning can be performed based on the total traffic amount of all edges of the combined bases and the sub-edge traffic amount of the bases combined thereafter, so that the traffic amount does not exceed the threshold. The time required to obtain the cut set can be shortened.

The network partitioning device according to claim 9 is characterized in that the number of nodes is used as an evaluation function of the subset of nodes.
Thereby, the difference in the number of nodes in each group obtained by dividing the network can be reduced, and as a result, the total management cost can be reduced.

  Further, according to the network partitioning program according to claim 10, the step of acquiring information relating to the connection relation between nodes constituting the network and the traffic amount flowing through each edge between the nodes, and the connection relation between the nodes Extracting a maximal tree of the network, calculating a base of a cocycle space belonging to the network from an edge of the maximal tree, and combining the bases so that the traffic amount does not exceed a threshold value. A step of calculating a cut set for dividing the network, a step of calculating a convex function as an evaluation function of a subset of nodes created from the cut set calculated by the cut set calculation means, and the evaluation function Based on the evaluation results obtained by Characterized in that and a step of presenting to the computer.

  As a result, it is possible to narrow down candidates for division whose spatial arrangement of nodes is evaluated without leaking candidates for network division whose traffic volume does not exceed the threshold. For this reason, it is possible to reduce the amount of traffic flowing between divided networks while considering the spatial arrangement of nodes, and even when the network is divided in consideration of the spatial arrangement of nodes. , Increase in calculation amount can be suppressed.

  As described above, according to the present invention, candidates for network division are extracted so that the amount of traffic flowing between the divided networks is reduced, and then the spatial arrangement of the nodes constituting the network is evaluated. As a result, it is possible to reduce the amount of traffic flowing between the divided networks while considering the spatial arrangement of the nodes, and to reduce the network management cost.

Hereinafter, a network dividing device and method according to an embodiment of the present invention will be described with reference to the drawings.
FIG. 1 is a functional block diagram showing a schematic configuration of a network dividing apparatus according to an embodiment of the present invention.
In FIG. 1, the network dividing device 10 extracts network division candidates based on the amount of traffic flowing between the divided networks, and the space of the nodes constituting the network with respect to the extracted network division candidates. Can be evaluated. Here, the network dividing device 10 is provided with a network information input unit 11, a maximal tree extraction unit 12, a base calculation unit 13, a cut set calculation unit 14, and a convex function calculation unit 15.

  The network information input means 11 inputs information related to the connection relationship between nodes constituting the network and the traffic volume flowing through each edge between the nodes. As the network, for example, a public communication network for performing IP communication can be used, and the Internet may be used. Further, it may be a private communication network between companies or a public communication network, but it is like an IP-VPN (Internet Protocol-Virtual Private Network) that can provide dedicated communication with high reliability and security. The Internet may be good. A node serves as a communication start point, end point, or relay point. Examples of nodes include a computer, a mobile terminal, and a router. The edge is a link between nodes, and examples of the edge include a communication medium such as an optical fiber and a coaxial cable, a wireless channel using a wireless interface, and the like. Each node can be given coordinates for specifying its spatial position, and each edge can be specified by designating nodes connected to both ends of the edge.

  The maximal tree extracting means 12 extracts a maximal tree of the network based on the connection relationship between the nodes. The maximal tree is a network without a loop in which edges are selected so as to cover the nodes of the network before the division. Here, the maximal tree extracting means 12 is provided with a maximal tree selecting means 12a, and the maximal tree selecting means 12a can select a maximal tree having the maximum total amount of edge traffic among the maximal trees of the network. it can.

  The basis calculation means 13 calculates the basis of the cocycle space belonging to the network from the edge of the maximal tree. The cocycle space is a space in which a symmetrical difference between cut sets of a certain network is closed as a calculation. Here, a cut set is a set of all edges that span between groups when the network is divided so that nodes constituting the network are divided into two groups. The symmetrical difference between the cut sets corresponds to exclusive OR, and when two cut sets are combined to form one cut set, the edges included in the two cut sets are mutually canceled, Extracting only edges included in one of the two cut sets. That is, an edge cut by an even number of cut sets is erased, and only an edge cut by an odd number of cut sets is left. A base is a cut set that can express all cut sets that divide a network by combining basic cut sets, and a cut set that includes only one edge of a maximal tree can be a base.

  The cut set calculation means 14 calculates a cut set for dividing the network by combining the bases so that the amount of traffic flowing between the divided networks does not exceed the threshold. Here, the cut set calculation unit 14 includes a combination order setting unit 14a, a tree generation unit 14b, and a pruning unit 14c.

  The combination order setting unit 14a can set the order of combining the bases based on at least one of the size of the traffic amount of the edge of the maximal tree and the number of edges of the base. The tree generation unit 14b can generate a tree that represents all combinations of bases according to the order in which the bases are combined. The pruning means 14c performs tree pruning based on the total traffic amount of the edges of the maximal tree possessed by the combined base, or adds the traffic amount of all the edges possessed by the combined base and thereafter. Trees can be pruned based on the presence or absence of sub-edges of the bases to be combined or the amount of traffic. The sub-edge is an edge that is not included in the maximal tree.

  For example, when the pruning means 14c combines the bases according to the order in which the bases are combined, if the total traffic amount at the edge of the maximal tree of the combined bases exceeds the threshold, the pruning means 14c selects a combination of bases lower than the bases. Can be omitted. Further, for example, when the pruning means 14c combines the bases according to the order in which the bases are combined, the total traffic amount of all the edges of the combined bases is eliminated due to the symmetric difference from the bases combined thereafter. If the threshold value is exceeded even after subtracting the traffic volume of the sub-edges that can be detected, combinations of bases lower than that base can be omitted.

The convex function calculation unit 15 calculates a convex function that is an evaluation function of a subset of nodes created from the cut set calculated by the cut set calculation unit 14. The convex function is a function for evaluating whether a subset of nodes and its complement are arranged spatially, and examples of the convex function include interclass variance.
FIG. 2 is a flowchart illustrating an example of a network partitioning method according to an embodiment of the present invention.

In FIG. 2, the network information input means 11 inputs network information related to the network to be divided into the network dividing device 10 (step S11). Here, the network information can include, for example, the coordinates of nodes constituting the network, information on edges connected between the nodes, information on the amount of traffic flowing through the edges, and the like.
When the network information is input to the network dividing device 10, the maximal tree extracting means 12 extracts the maximal tree of the network from the network information (step S12). Here, by extracting the maximal tree of the network, the base can be easily obtained, and an increase in the amount of calculation necessary for obtaining the base can be suppressed.

  When obtaining a maximal tree, it is preferable to select the maximal tree that maximizes the total amount of edge traffic. This makes it possible to increase the amount of traffic at the edge of a maximal tree, and when obtaining cut sets by sequentially combining bases, the edge of a maximal tree with a large amount of traffic can be incorporated into the cut set at an earlier stage. It becomes possible. For this reason, when the number of combinations of bases is smaller, a cut set whose traffic amount exceeds the threshold can be obtained, and subsequent base combinations for obtaining the cut set can be made unnecessary. As a result, it is possible to reduce the amount of calculation for obtaining network division candidates without leaking network division candidates whose traffic volume does not exceed the threshold, while suppressing deterioration in network division accuracy, The network can be divided efficiently.

  Next, when the maximal tree of the network is extracted by the maximal tree extracting unit 12, the basis calculating unit 13 calculates the basis of the cocycle space belonging to the network from the edge of the maximal tree (step S13). Here, by calculating the base, all cut sets that divide the network using the base cut set can be obtained, and the network division candidates are extracted without omission while suppressing an increase in the amount of calculation. can do.

  Next, when the base is calculated by the base calculation unit 13, the cut set calculation unit 14 combines the bases so that the amount of traffic flowing between the divided networks does not exceed the threshold, thereby cutting the network to be divided. A set is calculated (step S14). Note that the amount of traffic flowing between the divided networks can be represented by the total amount of traffic flowing through the edges included in the cut set dividing the network.

  As a result, network segmentation candidates whose traffic volume does not exceed the threshold can be extracted without omission, and for all network segmentation candidates whose traffic volume does not exceed the threshold, the node spatial It is possible to evaluate the correct arrangement. For this reason, it is possible to narrow down the candidates for division whose spatial arrangement of nodes is evaluated, it is possible to reduce the calculation amount of the convex function, and the network division so that the traffic amount does not exceed the threshold value Can be prevented from spilling from the evaluation target of the spatial arrangement of the nodes, and the network can be efficiently divided while suppressing the degradation of the network division accuracy.

  Next, when a cut set whose traffic volume does not exceed the threshold is calculated by the cut set calculation unit 14, the convex function calculation unit 15 is a convex function that is an evaluation function of a subset of nodes created from the cut set. A function is calculated (step S15). As a result, it is possible to evaluate the spatial arrangement of the nodes constituting the network after extracting network division candidates so that the amount of traffic flowing between the divided networks is reduced. For this reason, it is possible to reduce the amount of traffic flowing between the divided networks while considering the spatial arrangement of the nodes, and the network management cost can be reduced.

When the convex function of the divided network is calculated by the convex function calculating means 15, for example, the cut set is sorted by the class distribution of the divided network, and the divided network is ranked and presented. (Step S16).
Note that the network information input means 11, the maximum tree extraction means 12, the base calculation means 13, the cut set calculation means 14, and the convex function calculation means 15 execute a program in which instructions for executing the processing performed by these means are described in a computer. This can be realized by executing the command.

  Then, if this program is stored in a storage medium such as a CD-ROM, the network information input means 11, the maximum tree extraction means 12, and the like are installed in the computer and the program is installed in the computer. The processing performed by the base calculation means 13, the cut set calculation means 14, and the convex function calculation means 15 can be realized. Moreover, this program can be easily spread by downloading this program via the Internet.

  Further, when causing a computer to execute a program in which instructions for performing processing performed by the network information input unit 11, the maximum tree extraction unit 12, the base calculation unit 13, the cut set calculation unit 14, and the convex function calculation unit 15 are described. It may be executed by a stand-alone computer or may be distributed to a plurality of computers connected to a network.

FIG. 3 is a diagram illustrating a configuration example of a network according to an embodiment of the present invention.
In FIG. 3, for example, the network includes nodes N1 to N7 and edges E1 to E9, an edge E1 is connected between the nodes N2 and N3, an edge E2 is connected between the nodes N1 and N3, and a node N1. , N4, the edge E3 is connected, the nodes N3, N4 are connected to the edge E4, the nodes N3, N5 are connected to the edge E5, the nodes N4, N5 are connected to the edge E6, An edge E7 is connected between the nodes N4 and N6, an edge E8 is connected between the nodes N5 and N7, and an edge E9 is connected between the nodes N6 and N7. Here, the traffic volume flowing through the edge E1 is 1, the traffic volume flowing through the edge E2 is 3, the traffic volume flowing through the edge E3 is 2, the traffic volume flowing through the edge E4 is 5, the traffic volume flowing through the edge E5 is 6, and the edge E6 It is assumed that the amount of traffic flowing through the edge E7 is 3, the amount of traffic flowing through the edge E7 is 3, the amount of traffic flowing through the edge E8 is 1, and the amount of traffic flowing through the edge E9 is 1.

FIG. 4 is a diagram illustrating an example of a maximal tree in the network of FIG.
In FIG. 4A, for example, edges E1, E2, E5, E6, E7, and E8 are extracted as the maximal tree of the network in FIG. Here, the network constituted by these edges E1, E2, E5, E6, E7, E8 covers all the nodes N1 to N7 constituting the network of FIG. 3 and is not a loop. A network composed of the edges E1, E2, E5, E6, E7, and E8 constitutes a maximal tree.
Since the traffic amounts of these edges E1, E2, E5, E6, E7, E8 are 1, 3, 6, 6, 1, 1, respectively, the edges E1, E2, E5, The total traffic volume of E6, E7, and E8 is 18.

On the other hand, in FIG. 4B, for example, the network constituted by the edges E1, E3, E4, E6, E8, E9 covers all the nodes N1 to N7 constituting the network of FIG. Therefore, the network constituted by these edges E1, E3, E4, E6, E8, and E9 can also constitute a maximal tree.
Since the traffic amounts of these edges E1, E3, E4, E6, E8, E9 are 1, 2, 5, 6, 1, 1, respectively, the edges E1, E3, E4, The total traffic volume of E6, E8, and E9 is 16.

  Then, the total traffic amount of the edges of all the maximal trees in the network of FIG. 3 is examined, and the maximal tree having the maximum total traffic amount of the edges can be selected from these maximal trees. For example, when the total traffic amount of the edges of all the maximal trees in the network of FIG. 3 is examined, the traffic amount of the maximal tree composed of the edges E1, E2, E5, E6, E7, and E8 is the largest. As the maximal tree of the network, a maximal tree composed of edges E1, E2, E5, E6, E7, and E8 can be selected. For example, the Kruskal algorithm or the Prim algorithm may be used without examining all the maximal trees in the network of FIG.

FIG. 5 is a diagram illustrating an example of a base when the maximal tree in FIG. 4A is set.
In FIG. 5, the cut set b1 extends over the edges E2 and E3 to divide the network into the group of the node N1 and the groups of the nodes N2 to N7 and includes only one edge E2 of the maximal tree. It becomes the element of. The cut set b2 spans the edges E3, E4, E6, and E9, thereby dividing the network into a group of nodes N1 to N3, N5, and N7 and a group of nodes N4 and N6, and the edge E6 of the maximal tree to 1 Since only books are included, it becomes the base element. The cut set b3 extends over the edges E3 to E5, thereby dividing the network into a group of nodes N1 to N3 and a group of nodes N4 to N7 and including only one edge E5 of the maximal tree. It becomes. The cut set b4 spans the edges E3, E4, E6, and E9, thereby dividing the network into a group of nodes N1 to N5 and N7 and a group of node N6 and including only one edge E7 of the maximal tree. , It becomes the base element. The cut set b5 spans the edge E1 to divide the network into a group of nodes N1, N3 to N7 and a group of node N2 and includes only one edge E1 of the maximal tree, and thus becomes a base element. . The cut set b6 divides the network into a group of nodes N1 to N6 and a group of node N7 by straddling the edges E8 and E9 and includes only one edge E8 of the maximal tree, and thus becomes a base element. .

The maximum tree in FIG. 4A includes six edges E1, E2, E5, E6, E7, and E8. Therefore, in these six cut sets b1 to b6, FIG. The base of the cocycle space belonging to the network of can be configured.
When the base cut sets b1 to b6 are extracted, all the cut sets that divide the network of FIG. 3 into two can be obtained by combining the base cut sets b1 to b6. Here, the cut set calculation unit 14 in FIG. 1 can combine the cut sets b1 to b6 serving as the base so that the traffic amount flowing between the divided networks does not exceed the threshold value. Then, the order of combining the base cut sets b1 to b6 is set so that the division of the network such that the traffic volume exceeds the threshold is obtained at a stage where the number of combinations of the base cut sets b1 to b6 is smaller. Can do.

For example, the combination order setting means 14a in FIG. 1 has the traffic volume and the base cut sets b1 to b6 of the edges E1, E2, E5, E6, E7, and E8 of the maximal tree in FIG. The order of combining the bases can be set based on at least one of the number of edges.
FIG. 6 is a diagram illustrating an example of bases sorted according to the amount of edge traffic included in the maximal tree of FIG.

In the cut sets b1 to b6 in FIG. 5, the traffic amounts of the edges E2, E6, E5, E7, E1, and E8 of the maximum trees included in the cut sets b1 to b6 are 3, 6, 6, 3, 1, 1. For this reason, when the order of the cut sets b1 to b6 is rearranged by the traffic amount of the edges E2, E6, E5, E7, E1, and E8 of the maximal tree, the order of combining the cut sets b1 to b6 serving as the basis of FIG. As shown in FIG. 6, b1_m → b2_m → b3_m → b4_m → b5_m → b6_m.
When the order of combining the cut sets b1_m to b6_m is obtained, the network is divided so that the traffic amount does not exceed the threshold by combining the cut sets b1_m to b6_m in the order of b1_m → b2_m → b3_m → b4_m → b5_m → b6_m. Find all the cut sets you want.

  Here, by setting the order of combining the cut sets b1_m to b6_m based on the traffic amount of the edges E1, E2, E5, E6, E7, and E8 of the maximal tree, the edge E1 of the maximal tree having a large traffic amount is set. , E2, E5, E6, E7, E8 can be incorporated into the cut set at an earlier stage. For this reason, it is possible to obtain a cut set in which the traffic amount exceeds the threshold value and the traffic amount does not become lower than the threshold value due to the symmetric difference between the bases thereafter when the number of base combinations is smaller. Therefore, when a cut set whose traffic amount does not exceed the threshold value is obtained, a wasteful combination of bases can be eliminated without leaking a cut set whose traffic amount does not exceed the threshold value. A cut set for dividing the network so as not to exceed the threshold can be efficiently obtained.

FIG. 7 is a diagram illustrating an example of a cut set generated by combining the bases of FIG.
In FIG. 7A, for example, it is assumed that the threshold of the traffic amount flowing between the divided networks is set to 10. When the cut set b1_m and the cut set b2_m are first combined, since the edges E3 and E4 are included in the cut sets b1_m and b2_m, the edges E3 and E4 are deleted, and only the edges E5, E6, and E9 are included. A cut set b1b2_m including is generated.

  Here, the edges E5 and E6 are included in the maximal tree, and the total traffic volume of these edges E5 and E6 is 12, so the traffic volume of the cut set b1b2_m exceeds the threshold = 10. In addition, since the base cut sets b1_m to b6_m include only one edge E6, E5, E2, E7, E1, and E8 of the maximal tree, any cut set b3_m in the cut set b1b2_m is included. Even when .about.b6_m is further combined, the edges E5 and E6 of the maximal tree included in the cut set b1b2_m are not erased. Therefore, even if the cut sets b3_m to b6_m are further combined with the cut set b1b2_m to generate a new cut set, the total traffic volume of the cut set does not become the threshold = 10 or less, and the cut set b1b2_m is further cut. The operation of combining the sets b3_m to b6_m can be omitted.

  On the other hand, as shown in FIG. 7B, when the cut set b1_m and the cut set b3_m are first combined, the edge E3 is included in the cut sets b1_m and b3_m, so the edge E3 is erased and the edge A cut set b1b3_m including only E2, E4, E6, and E9 is generated. Here, the edges E2 and E6 are included in the maximal tree, and the total traffic volume of these edges E2 and E6 is 9, so the traffic volume of the cut set b1b3_m is equal to or less than the threshold = 10. Therefore, at the stage where the cut set b1_m and the cut set b3_m are combined, if a new cut set is generated by further combining the cut sets b2_m and b4_m to b6_m with the cut set b1b3_m, the total traffic amount of the cut set is the threshold value. = 10 or less, there is a need to perform an operation for further combining the cut sets b2_m and b4_m to b6_m with the cut set b1b3_m.

  Therefore, even when a new cut set is generated by further combining the cut set b1b3_m with the cut set b2_m, the total traffic amount of the cut set does not become the threshold = 10 or less, but the cut set b1_m When the cut set b3_m is first combined, it is necessary to perform an operation of further combining the cut set b1_b3_m with the cut set b2_m, resulting in a wasteful combination operation.

  On the other hand, when the cut set b1_m and the cut set b2_m are first combined, the total traffic amount is obtained even if the cut sets b3_m to b6_m are further combined with the cut set b1b2_m when the cut set b1_m and the cut set b2_m are combined. Therefore, it can be determined that there is no need to perform an operation for further combining the cut sets b3_m to b6_m with the cut set b1b2_m.

  Therefore, by setting the order of combining the cut sets b1_m to b6_m based on the traffic amount of the edges E1, E2, E5, E6, E7, and E8 of the maximal tree, the traffic amount does not exceed the threshold value. Without leaking the combinations of the cut sets b1_m to b6_m, the number of combinations of the cut sets b1_m to b6_m can be reduced, and the network can be efficiently divided so that the traffic amount does not exceed the threshold value.

FIG. 8 is a diagram illustrating an example of bases sorted by the number of edges that the base of FIG. 5 has.
In the cut sets b1 to b6 in FIG. 5, the cut set b1 includes edges E2 and E3, the cut set b2 includes edges E3, E4, E6, and E9, and the cut set b3 includes edges E3 to E5. The cut set b4 includes edges E3, E4, E6, and E9, the cut set b5 includes edge E1, and the cut set b6 includes edges E8 and E9. For this reason, the number of edges of the base cut sets b1 to b6 are 2, 4, 3, 4, 1, and 2, respectively. Therefore, when the order of the cut sets b1 to b6 is rearranged according to the number of edges that each of the cut sets b1 to b6 has, the order of combining the cut sets b1 to b6 that are the basis of FIG. 5 is b1_s → b2_s → b3_s → b4_s → b5_s → b6_s.

When the order of combining the cut sets b1_s to b6_s is obtained, the network is divided so that the traffic amount does not exceed the threshold by combining the cut sets b1_s to b6_s in the order of b1_s → b2_s → b3_s → b4_s → b5_s → b6_s. Ask all.
Here, by setting the order of combining the cut sets b1_s to b6_s based on the number of edges of the base cut sets b1 to b6, more sub-edges are incorporated into the cut sets b1_s to b6_s at an earlier stage. Therefore, the number of sub-edges that can be erased due to the difference in the basis symmetry can be reduced at a stage where the number of base combinations is smaller. For this reason, when a cut set whose traffic volume exceeds the threshold value is obtained, a cut set in which the traffic volume does not fall below the threshold value regardless of the combination of the subsequent bases is obtained at a stage where the number of base combinations is smaller. Therefore, it is possible to efficiently divide the network so that the traffic amount does not exceed the threshold value without using the combination of the subsequent bases when obtaining the cut set.

FIG. 9 is a diagram illustrating an example of a cut set generated by combining the bases of FIG.
In FIG. 9A, for example, it is assumed that the threshold of the traffic amount flowing between the divided networks is set to 10. Then, when the cut set b1_s and the cut set b2_s are first combined, a cut set b1b2_s including the edges E5, E6, and E9 is generated.

  Here, the traffic volumes of the edges E5, E6, and E9 are 6, 6, and 1, respectively, and the total traffic volume of these edges E5, E6, and E9 is 13, so the traffic volume of the cut set b1b2_s is the threshold = 10 is exceeded. Here, since the cut set b1b2_s includes the sub-edge E9, when the cut sets b3_s to b6_s are further combined with the cut set b1b2_s, the edge that may be erased by the calculation of the symmetric difference is E9. . However, the traffic amount of the edge E9 is 1, and even if the sub-edge E9 of the cut set b1b2_s is deleted, the traffic amount of the entire cut set b1b2_s does not become the threshold value = 10 or less. Therefore, even if a new cut set is generated by further combining the cut sets b1_2 to b6_s with the cut set b1b2_s, the total traffic amount of the cut sets does not become the threshold = 10 or less, and the cut set b1b2_s is further cut. The operation of combining the sets b3_s to b6_s can be omitted.

  On the other hand, as shown in FIG. 9B, when the cut set b1_s and the cut set b3_s are first combined, the cut set b1b3_s including the edges E2, E4, E6, and E9 is generated. Here, the traffic volume of the edges E2, E4, E6, and E9 is 3, 5, 6, and 1, respectively, and the total traffic volume of these edges E2, E4, E6, and E9 is 15, so the cut set b1b3_s The amount of traffic exceeds the threshold = 10. Here, since the cut set b1b3_s includes sub-edges E4 and E9, when the cut sets b2 and b4 to b6 are further combined with the cut set b1b3_s, the edges that may be deleted by the calculation of the symmetric difference are E4 and E9, but the traffic amounts of the edges E4 and E9 are 5 and 1, respectively. For this reason, at the stage where the cut set b1_s and the cut set b3_s are combined, if a new cut set is generated by further combining the cut sets b1_3 and b4_s to b6_s with the cut set b1b3_s, the total traffic amount of the cut sets is the threshold value. = 10 or less, there is a need to perform an operation of further combining the cut sets b2_s and b4_s to b6_s with the cut set bb3_s.

  Therefore, even if the cut set b2_s is further combined with the cut set b2_s to generate a new cut set, the total traffic amount of the cut set does not fall below the threshold = 10, but the cut set b1_s When the cut set b3_s is first combined, it is necessary to perform an operation of further combining the cut set b2_s with the cut set b1b3_s, resulting in a wasteful combination operation.

  On the other hand, when the cut set b1_s and the cut set b2_s are first combined, even if the cut sets b3_s to b6_s are further combined with the cut set b1b2_s at the stage of combining the cut set b1_s and the cut set b2_s, the total traffic amount Therefore, it can be determined that there is no need to perform an operation for further combining the cut sets b3_s to b6_s with the cut sets b1b2_s. Therefore, by setting the order in which the cut sets b1_s to b6_s are combined based on the number of edges of the base cut sets b1 to b6, combinations of the cut sets b1_s to b6_s that do not exceed the threshold value are set. Without leaking, the number of combinations of the cut sets b1_s to b6_s can be reduced, and the network can be efficiently divided so that the traffic amount does not exceed the threshold value.

FIG. 10 is a diagram illustrating an example of bases sorted according to the amount of edge traffic included in the maximal tree of FIG. 4 for the same number of edges of the base of FIG.
In the cut sets b1_s to b6_s in FIG. 5, the number of edges of the base cut sets b1_s to b6_s is 4, 4, 3, 2, 2, 1 respectively. For this reason, the cut sets b1_s and b2_s each have 4 edges, which are equal to each other. Further, the number of edges of the cut sets b4_s and b5_s is 2 and equal to each other. For this reason, for the cut sets b1_s and b2_s having the same number of edges, the cut sets b1_s and b2_s are rearranged according to the traffic amount of the edges E6 and E5 included in the maximal trees included in the cut sets b1_s and b2_s. The cut sets b4_s and b5_s are rearranged according to the traffic amount of the edges E7 and E8 included in the maximal tree included in each of the cut sets b4_s and b5_s. As a result, the order of combining the cut sets b1 to b6 serving as the basis of FIG. 5 is as follows: b1_ms → b2_ms → b3_ms → b4_ms → b5_ms → b6_ms.

FIG. 11 is a diagram illustrating an example of an order of combining bases according to an embodiment of the present invention.
In FIG. 11, if the tree generation means 14b of FIG. 1 combines the cut sets b1 to b6 of FIG. 5 in the order of b1, b2, b3, b4, b5, b6, for example, b1 → b2 → b3 → b4. A tree branched in the order of b5 b6 is generated. Then, by combining the cut sets b1 to b6 in the depth-first search in order from the left, all cut sets combined in the order of b1, b2, b3, b4, b5, and b6 can be generated. For example, a portion indicated by □ is a cut set b1b3b4 in which cut sets b1, b3, and b4 are combined, and a portion indicated by ◯ is a cut set b2b4b5b6, in which cut sets b2, b4, b5, and b6 are combined. The indicated part shows a cut set b4 including only the cut set b4.

FIG. 12 is a diagram showing an example of execution results of the combination of bases and pruning according to an embodiment of the present invention.
In FIG. 12, the threshold value of the traffic amount flowing between the divided networks is set to 10, and the cut sets b1 to b6 in FIG. 5 are combined in the order of b1 → b2 → b3 → b4 → b5 → b6.

  Here, the cut sets b2 and b3 include edges E6 and E5 of maximal trees, respectively, and the traffic amounts of these edges E6 and E5 are 6 and 6, respectively. Therefore, when the cut set b2b3 is generated by combining the cut sets b2 and b3, the total traffic amount of the edges E6 and E5 of the maximal tree of the cut set b2b3 is 12. Therefore, the total traffic amount of the edges E6 and E5 of the maximal tree of the cut set b2b3 exceeds the threshold = 10, and even if a cut set is generated by further combining the cut sets b4, b5, and b6 with the cut set b2b3, the cut It can be determined that the traffic volume of the set does not become the threshold = 10 or less. Therefore, pruning K1 and K4 of the cut sets b4, b5, and b6 (ranges R1 and R4) that are lower than the cut sets b2 and b3 can be performed, and the cut sets b4, b5, and b6 are further added to the cut set b2b3. The combining operation can be omitted.

  Further, since the cut set b1 includes edges E2 and E3, and the cut set b2 includes edges E3, E4, E6, and E9, when the cut sets b1 and b2 are combined, the edges E2, E4, E6, and E9 are combined. A cut set b1b2 is generated. Since the traffic amounts of the edges E2, E4, E6, and E9 are 3, 5, 6, and 1, respectively, the traffic amount of the entire cut set b1b2 is 15, and the traffic amount of the entire cut set b1b2 exceeds the threshold = 10. . Here, since the cut set b1b2 includes sub-edges E4 and E9, when the cut sets b4, b5, and b6 are further combined with the cut set b1b2, the edges that may be deleted by the calculation of the symmetric difference are E4 and E9. However, the edge E4 is not included in the cut sets b4, b5, and b6, and even if the cut sets b4, b5, and b6 are further combined with the cut set b1b2, the sub-edge E4 of the cut set b1b2 is not erased. . Further, the traffic amount of the edge E9 is 1, and even if the sub-edge E9 of the cut set b1b2 is deleted, the traffic amount of the entire cut set b1b2 does not become the threshold value = 10 or less.

  Therefore, even if a cut set in which the cut sets b4, b5, and b6 are further combined with the cut set b1b2 is generated, it can be determined that the traffic amount of the cut set does not become the threshold value = 10 or less. Therefore, the pruning K2 of the cut sets b4, b5, b6 (range R2) lower than the cut sets b1, b2 can be performed, and the operation of further combining the cut sets b4, b5, b6 with the cut set b1b2 is omitted. can do.

  In addition, since the cut set b1 includes edges E2 and E3, and the cut set b3 includes edges E3, E4, and E5, when the cut sets b1 and b3 are combined, a cut that includes the edges E2, E4, and E5 A set b1b3 is generated. Since the traffic amounts of the edges E2, E4, and E5 are 3, 5, and 6, respectively, the traffic amount of the entire cut set b1b3 is 14, and the traffic amount of the entire cut set b1b3 exceeds the threshold = 10. Here, since the sub-edge E4 is included in the cut set b1b3, when the cut sets b4, b5, and b6 are further combined with the cut set b1b3, the edge that may be deleted by the calculation of the symmetric difference is E4. is there. However, the edge E4 is not included in the cut sets b4, b5, and b6, and even if the cut sets b4, b5, and b6 are further combined with the cut set b1b3, the sub-edge E4 of the cut set b1b3 is not erased. .

  Therefore, even if a cut set in which the cut sets b4, b5, and b6 are further combined with the cut set b1b3 is generated, it can be determined that the traffic amount of the cut set does not become the threshold value = 10 or less. Therefore, the pruning K3 of the cut sets b4, b5, b6 (range R3) lower than the cut sets b1, b3 can be performed, and the operation of further combining the cut sets b4, b5, b6 with the cut set b1b3 is omitted. can do.

  The cut set b2 includes edges E3, E4, E6, and E9. Since the traffic amounts of the edges E3, E4, E6, and E9 are 2, 5, 6, and 1, respectively, the traffic amount of the entire cut set b2 is 14, and the traffic amount of the entire cut set b2 exceeds the threshold = 10. . Here, since the sub-edges E3, E4, and E9 are included in the cut set b2, when the cut sets b4, b5, and b6 are further combined with the cut set b2, there is a possibility that the cut set b2 may be erased by calculating the symmetrical difference. The edges are E3, E4, and E9. However, the edge E4 is not included in the cut sets b4, b5, and b6, and even if the cut sets b4, b5, and b6 are further combined with the cut set b1b2, the sub-edge E4 of the cut set b1b2 is not erased. . Further, the traffic amounts of the edges E3 and E9 are 2 and 1, respectively, and even if the sub-edges E3 and E9 of the cut set b2 are deleted, the traffic amount of the entire cut set b2 does not become the threshold value = 10 or less.

  Therefore, even if a cut set in which the cut sets b4, b5, and b6 are further combined with the cut set b2 is generated, it can be determined that the traffic amount of the cut set does not become the threshold value = 10 or less. Therefore, the pruning K5 of the cut sets b4, b5, and b6 (range R5) lower than the cut set b2 can be performed, and the operation of further combining the cut sets b4, b5, and b6 with the cut set b2 is omitted. Can do.

  The cut set b3 includes edges E3, E4, and E5. Since the traffic amounts of the edges E3, E4, and E5 are 2, 5, and 6, respectively, the traffic amount of the entire cut set b3 is 13, and the traffic amount of the entire cut set b3 exceeds the threshold = 10. Here, since the cut set b3 includes the sub-edges E3 and E4, when the cut set b3 is further combined with the cut sets b4, b5, and b6, the edge that may be deleted by the calculation of the symmetric difference is E3 and E4. However, the edge E4 is not included in the cut sets b4, b5, and b6, and even if the cut sets b4, b5, and b6 are further combined with the cut set b3, the sub-edge E4 of the cut set b3 is not erased. . Further, the traffic amount of the edge E3 is 2, and even if the sub-edge E3 of the cut set b3 is deleted, the traffic amount of the entire cut set b3 does not become the threshold value = 10 or less.

  Therefore, even if a cut set in which the cut sets b4, b5, and b6 are further combined with the cut set b3 is generated, it can be determined that the traffic amount of the cut set does not become the threshold value = 10 or less. Therefore, pruning K6 can be performed on the cut sets b4, b5, and b6 (range R6) that are lower than the cut set b3, and the operation of further combining the cut sets b4, b5, and b6 with the cut set b3 is omitted. Can do.

FIG. 13 is a diagram illustrating an example of pruning when the order of combining bases according to an embodiment of the present invention is changed.
In FIG. 13, it is assumed that the threshold of the traffic amount flowing between the divided networks is set to 10, and the cut sets b1 to b6 of FIG. 5 are combined in the order of b5 → b6 → b1 → b2 → b3 → b4. In this case, the underlying elements that cause pruning K11 are combined towards the end of the tree. For this reason, it turns out that the frequency | count that the combination operation of a cut set can be abbreviate | omitted by pruning K11 decreases.

  For example, the cut set b5 includes the edge E1, and the cut set b6 includes the edges E8 and E9. Therefore, when the cut sets b5 and b6 are combined, the cut set b5b6 including the edges E1, E8, and E9 is generated. Is done. Since the traffic volumes of the edges E1, E8, and E9 are 1, 1, and 1, respectively, the traffic volume of the entire cut set b5b6 is 3, and the traffic volume of the entire cut set b5b6 is equal to or less than the threshold = 10. For this reason, if a cut set in which the cut sets b1, b2, b3, and b4 are further combined with the cut set b5b6 is generated, the traffic amount of the cut set may be equal to or less than the threshold = 10. A cut set b5b6b1 is generated by combining the cut sets b1.

  Here, since the cut set b1 includes edges E2 and E3, when the cut set b1 is further combined with the cut set b5b6, a cut set b5b6b1 including the edges E1, E2, E3, E8, and E9 is generated. The traffic volume of the cut set b5b6bb1 is 8. For this reason, the traffic amount of the cut set b5b6bb1 is equal to or less than the threshold value = 10, and when a cut set in which the cut sets b2, b3, and b4 are further combined with the cut set b5b6b1 is generated, the traffic amount of the cut set becomes the threshold value = 10 or less. Since there is a possibility, the cut set b5b6b1b2 is generated by further combining the cut set b2 with the cut set b5b6b1.

  Here, since the cut set b2 includes the edges E3, E4, E6, and E9, when the cut set b2 is further combined with the cut set b5b6b1, the cut set that includes the edges E1, E2, E4, E6, and E8. b5b6b1b2 is generated, and the traffic volume of the cut set b5b6b1b2 is 16. Here, of the edges E1, E2, E4, E6, and E8 included in the cut set b5b6bb1, the edges E1, E2, E6, and E8 are included in the maximal tree, and the edges E1, E2, and E6 of the maximal tree of the cut set b5b6b1b2 are included. The total traffic volume of E8 is 11.

  Therefore, even if the total traffic amount of the edges E1, E2, E6, and E8 of the maximal tree of the cut set b5b6bb1b2b exceeds the threshold = 10, and the cut set that further combines the cut sets b3 and b4 with the cut set b5b6b1b2 is generated, It can be determined that the traffic volume of the cut set does not become the threshold = 10 or less. Therefore, the pruning K11 of the cut sets b3, b4 (range R11) lower than the cut sets b5, b6, b1, b2 can be performed, and the cut sets b3, b4 are added to the cut sets b5, b6, b1, b2. The operation of further combining the can be omitted.

Thus, it turns out that the frequency | count of combination of the cut sets b1-b6 which can perform pruning changes with the order which combines the cut sets b1-b6. In order to enable pruning at a stage where the number of combinations of the cut sets b1 to b6 is small, based on at least one of the size of the traffic amount of the edge of the maximal tree and the number of edges of the base Thus, it is preferable to set the order of combining the bases.
When a cut set whose traffic amount does not exceed the threshold value is calculated, a convex function that is an evaluation function of a subset of nodes created from the cut set is calculated. Here, as the convex function, for example, as shown in the following formula, inter-class variance can be used. As the inter-class variance value is larger, it can be regarded as a group that is largely divided.

Where V is a set of all nodes, X is a subset of nodes, X bar is a complement of a subset of nodes, c (X) is the centroid of X, d (x, y) is a node of x and y This represents the distance between x and y with the coordinates of.
When evaluating whether a group of nodes of the network obtained by the division is largely divided, the number of nodes may be used as an evaluation function of a subset of nodes.

In order to evaluate the effect of the present invention, a simulation was performed using a randomly created network. Here, the network was created as follows.
First, the maximum number of nodes and edges and the traffic volume were set. The number of edges is greater than or equal to the number of nodes and less than or equal to 10 times the number of nodes. Next, nodes were randomly arranged in a 600 × 600 two-dimensional space, followed by edges. Here, in order to be close to the actual network, we first created a maximal tree that minimizes the total edge distance. Then, the remaining edges are arranged so that randomly selected nodes are connected to nearby nodes. Finally, the traffic volume at each edge was set at random so that the traffic volume was below the maximum value.

FIG. 14 is a diagram showing an example of a network used for the evaluation of the present invention.
In the example of FIG. 14, the number of nodes is 100, the number of edges is 150, and the maximum traffic amount is 10. The number given on the edge in FIG. 14 is the traffic amount.
FIG. 15 is a diagram illustrating an example of division of the network of FIG.
In FIG. 15, a cut set KS in which the traffic amount is set to 15 and the traffic amount flowing between the divided networks does not exceed the threshold value so that the inter-class variance value of the nodes constituting the network becomes the largest. Asked. Here, the cut set KS includes edges E11 and E12 of the maximal tree and sub-edges E13 and E14. In the example of FIG. 15, 10676 subsets of nodes having cut sets in which the amount of traffic flowing between the divided networks does not exceed threshold = 15 are obtained. In the example of FIG. 15, it can be seen that the group of nodes obtained by dividing the network is divided and arranged while maintaining a spatial unity.

FIG. 16 is a diagram illustrating a comparative example of the time taken to create a cut set whose traffic volume is equal to or less than a threshold value due to a difference in a maximal tree. Note that the columns in FIG. 16 indicate network creation conditions. Further, the row in FIG. 16 shows in ms the time taken to divide a node having a cut set whose traffic volume is equal to or less than a threshold when a network is created 10 times at random.
In FIG. 16, assuming that the number of nodes is 100, the number of edges is 150, and the traffic amount threshold is 10, the case where the maximal tree that maximizes the total traffic amount of the edges is selected is compared to the case where it is not so. Thus, it can be seen that the time taken to divide a node having a cut set whose traffic volume is equal to or less than the threshold value is substantially reduced. Also, assuming that the number of nodes is 300, the number of edges is 600, and the threshold of traffic volume is 10, the traffic depending on whether the maximum tree having the maximum total traffic volume of the edge is selected or not. It can be seen that the time taken to divide a node having a cut set whose amount is equal to or less than the threshold can be reduced by an order of magnitude, and that the effect is increased when the number of nodes is large.

  In addition, even when the number of nodes is 100, the number of edges is 400, and the traffic amount threshold is 40, if the maximal tree that maximizes the total traffic amount of the edges is selected, the traffic amount is less than the threshold. It can be seen that the time taken to divide a node having a cut set becomes smaller, and that it has a certain effect even when the number of edges is large.

FIG. 17 is a diagram illustrating a comparative example of the time taken to create the base due to the difference in the maximal tree. In the example of FIG. 17, the network creation conditions are the same as those in the example of FIG. 16, and the time taken to create the base is shown in ms.
In FIG. 17, when the maximal tree having the maximum amount of traffic at the edge is selected, the time required to create the base is increased compared to the case where the maximum is not so, and when the number of nodes is increased, the difference is as follows. It turns out that it grows. However, selecting the maximal tree that maximizes the amount of traffic on the edge increases the time taken to create the bases, but the time taken to combine the bases is further reduced and the time taken to divide the network is reduced. As can be reduced.

  FIG. 18 is a diagram illustrating a comparative example of the time taken to create a cut set whose traffic amount is equal to or less than a threshold value due to the difference in the order of bases. In the example of FIG. 17, the network creation conditions are the same as those in the example of FIG. 16, and when the network is randomly created only 10 times, it takes time to divide a node having a cut set whose traffic volume is equal to or less than the threshold. The time was shown in ms. In the first, fourth, and seventh embodiments, the order of combining the bases is set based on the traffic amount of the edge of the maximal tree. In the second, fifth, and eighth embodiments, the order of the edges of the bases is set. The order of combining the bases is set. In the third, sixth, and ninth embodiments, the order of combining the bases is set based on the size of the traffic amount of the edge of the maximal tree, and the size of the traffic amount of the edge of the maximal tree is set. For the same thing, the order of combining the bases was set based on the number of edges of the bases.

  In FIG. 18, by setting the order of combining the bases based on the size of the traffic amount of the edge of the maximal tree or the number of edges of the base, it is possible to reduce the time taken to create a cut set whose traffic amount is equal to or less than the threshold value. I understand. It can also be seen that the effect is great if the order of combining bases is set based on both the amount of traffic at the edges of the maximal tree and the number of edges of the bases.

  The present invention can be used not only for dividing and managing a network such as the Internet but also for dividing an ad hoc network in which a mobile host group having a wireless interface locally forms a temporary network.

It is a functional block diagram which shows schematic structure of the network division | segmentation apparatus which concerns on one Embodiment of this invention. It is a flowchart which shows an example of the network division | segmentation method which concerns on one Embodiment of this invention. It is a figure which shows the structural example of the network which concerns on one Embodiment of this invention. It is a figure which shows the example of the maximum tree in the network of FIG. It is a figure which shows the example of a base when the maximum tree of Fig.4 (a) is set. It is a figure which shows the example of the base sorted by the magnitude | size of the traffic amount of the edge contained in the maximal tree of Fig.4 (a). It is a figure which shows the example of the cut set produced | generated by combining the base of FIG. It is a figure which shows the example of the base sorted by the edge number which the base of FIG. 5 has. It is a figure which shows the example of the cut set produced | generated by combining the base of FIG. FIG. 9 is a diagram illustrating an example of bases sorted according to the amount of traffic of edges included in the maximal tree of FIG. 4 with respect to the same number of edges in the base of FIG. 8. It is a figure which shows an example of the order which combines the base which concerns on one Embodiment of this invention. It is a figure which shows an example of the execution result and pruning of the combination of the base which concerns on one Embodiment of this invention. It is a figure which shows an example of pruning when the order which combines the base which concerns on one Embodiment of this invention is changed. It is a figure which shows an example of the network used for evaluation of this invention. It is a figure which shows the example of a division | segmentation of the network of FIG. It is a figure which shows the comparative example of the time concerning creation of the cut set whose traffic amount by the difference of local maximum trees is below a threshold value. It is a figure which shows the comparative example of the time concerning creation of the base by the difference in the maximum tree. It is a figure which shows the comparative example of the time concerning preparation of the cut set whose traffic amount by the difference in the order of a base is below a threshold value.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Network dividing device 11 Network information input means 12 Maximum tree extraction means 12a Maximum tree selection means 13 Base calculation means 14 Cutset calculation means 14a Combination order setting means 14b Tree generation means 14c Pruning means 15 Convex function calculation means N1 to N7 nodes E1 to E9 Edge b1 to b6, b1_m to b6_m, b1b3b5_m, b2b6_m, b1_s to b6_s, b1_ms to b6_ms Cutset

Claims (10)

Division candidate extraction means for extracting candidates for division of the network based on the amount of traffic flowing between the divided networks;
A network partitioning apparatus comprising: a node placement evaluation unit that evaluates a spatial placement of nodes constituting the network with respect to the network partition candidate extracted by the partition candidate extraction unit. The division candidate extraction means includes
Network information input means for inputting information relating to the connection relationship between the nodes constituting the network and the amount of traffic flowing through each edge between the nodes;
Maximal tree extracting means for extracting a maximal tree of the network based on a connection relation between the nodes;
Basis calculation means for calculating a basis of a cocycle space belonging to the network from an edge of the maximal tree;
A cut set calculating means for calculating a cut set for dividing the network by combining the bases so that the traffic amount does not exceed a threshold;
The node arrangement evaluation means includes:
2. The network dividing apparatus according to claim 1, further comprising a convex function calculating unit that calculates a convex function that is an evaluation function of a subset of nodes created from the cut set calculated by the cut set calculating unit. The maximum tree extracting means includes:
3. The network dividing apparatus according to claim 2, further comprising: a maximal tree selecting unit that selects a maximal tree having a maximum total amount of edge traffic among the maximal trees of the network. The cut set calculation means includes
4. The combination order setting means for setting a combination order of bases based on at least one of the size of the traffic amount of the edge of the maximal tree and the number of edges of the bases. Network partition device. The cut set calculation means includes
Tree generating means for generating a tree representing all combinations of the bases according to the order of combining the bases;
5. The network partition according to claim 2, further comprising a pruning unit that prunes the tree based on a total traffic amount of edges of the maximal tree included in the combined base. apparatus.   The pruning means omits a combination of bases lower than the base when the total traffic amount of the edge of the maximal tree of the combined base exceeds a threshold when the bases are combined in the order in which the bases are combined. 6. The network dividing apparatus according to claim 5, wherein The cut set calculation means includes
Tree generating means for generating a tree representing all combinations of the bases according to the order of combining the bases;
Pruning means is provided for pruning the tree based on the total traffic amount of all edges of the combined bases and the presence or absence of sub-edges of the bases combined thereafter or the traffic amount. The network dividing device according to any one of claims 2 to 4.   In the pruning means, when the bases are combined according to the order in which the bases are combined, the total traffic amount of all edges of the combined bases may be erased due to a symmetric difference from the bases combined thereafter. 8. The network dividing apparatus according to claim 7, wherein when a traffic amount of a certain sub-edge is subtracted and the threshold value is exceeded, a combination of bases lower than the base is omitted.   9. The network dividing device according to claim 2, wherein the number of nodes is used as an evaluation function of the subset of nodes. Obtaining information relating to the connection relationship between nodes constituting the network and the amount of traffic flowing through each edge between the nodes;
Extracting a maximal tree of the network based on a connection relationship between the nodes;
Calculating a base of a cocycle space belonging to the network from an edge of the maximal tree;
Calculating a cut set for dividing the network by combining the bases so that the traffic volume does not exceed a threshold; and
Calculating a convex function which is an evaluation function of a subset of nodes created from the cut set calculated by the cut set calculation means;
A network partitioning program that causes a computer to execute a step of presenting a network partitioning position based on an evaluation result obtained by the evaluation function.

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