### Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 34-41 |

Number of pages | 8 |

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

Volume | 82 |

Issue number | 12 |

Publication status | Published - Dec 1999 |

Externally published | Yes |

### Fingerprint

### Keywords

- FM method
- Graph partitioning problem
- KL method
- Neural network
- NP hard
- Operating equation
- Shaking term

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

**A Binary Neural Network Algorithm for the Graph Partitioning Problem.** / Tamaki, Yasuhiro; Funabiki, Nobuo; Nishikawa, Seishi.

Research output: Contribution to journal › Article

*Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)*, vol. 82, no. 12, pp. 34-41.

}

TY - JOUR

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

AU - Tamaki, Yasuhiro

AU - Funabiki, Nobuo

AU - Nishikawa, Seishi

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 - Neural network

KW - NP hard

KW - Operating equation

KW - Shaking term

UR - http://www.scopus.com/inward/record.url?scp=0346549650&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0346549650&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0346549650

VL - 82

SP - 34

EP - 41

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 -