TY - JOUR

T1 - A Binary Neural Network Algorithm for the Graph Partitioning Problem

AU - Tamaki, Yasuhiro

AU - Funabiki, Nobuo

AU - Nishikawa, Seishi

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 1999/12

Y1 - 1999/12

N2 - The graph partitioning problem is an NP hard problem of deriving the partitioning of each vertex such that the total stun of the edge weights among the groups is minimized and the total sum of the vertex weights in each group is less than the upper limit. In this paper, a neural network solution is proposed in which the binary neurons are used for the graph 2-partitioning problem. In the present neural network, an energy function that is applicable to graphs both with and without edge and vertex weights is defined. For improvement of solution accuracy, shaking terms are introduced into the operating equation. To evaluate the solution search capability of the present method, simulations are carried out for random graphs, together with the KL method proposed by Kernighan and Lin, and the FM method proposed by Fiduccia and Mattheyses. From the simulation results, it is shown that the solutions obtained by the present method are the best.

AB - The graph partitioning problem is an NP hard problem of deriving the partitioning of each vertex such that the total stun of the edge weights among the groups is minimized and the total sum of the vertex weights in each group is less than the upper limit. In this paper, a neural network solution is proposed in which the binary neurons are used for the graph 2-partitioning problem. In the present neural network, an energy function that is applicable to graphs both with and without edge and vertex weights is defined. For improvement of solution accuracy, shaking terms are introduced into the operating equation. To evaluate the solution search capability of the present method, simulations are carried out for random graphs, together with the KL method proposed by Kernighan and Lin, and the FM method proposed by Fiduccia and Mattheyses. From the simulation results, it is shown that the solutions obtained by the present method are the best.

KW - FM method

KW - Graph partitioning problem

KW - KL method

KW - NP hard

KW - Neural network

KW - Operating equation

KW - Shaking term

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U2 - 10.1002/(sici)1520-6440(199912)82:12<34::aid-ecjc4>3.0.co;2-5

DO - 10.1002/(sici)1520-6440(199912)82:12<34::aid-ecjc4>3.0.co;2-5

M3 - Article

AN - SCOPUS:0346549650

VL - 82

SP - 34

EP - 42

JO - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)

JF - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)

SN - 1042-0967

IS - 12

ER -