Computer Science ›› 2020, Vol. 47 ›› Issue (1): 72-78.

• Computer Science Theory •

### Quick Algorithm to Find an Approximate Maximum Clique in Undirected Graph by Using Local-limited Search Strategy

ZHONG Mao-sheng1,2,JIANG Chao2,TAO Lan2,HE Xiong2,LUO Yuan-sheng3

1. (School of Computer & Information Engineering,Jiangxi Normal University,Nanchang 330022,China)1;
(School of Information Engineering,East China Jiaotong University,Nanchang 330013,China)2;
(Center of Network Information Management,Jiangxi University of Finance and Economics,Nanchang 330013,China)3
• Received:2018-11-15 Published:2020-01-19
• About author:ZHONG Mao-sheng,Ph.D,professor,master supervisor.His research intere-sts include graph theory,algorithm design,social network and natural language processing.
• Supported by:
This work was supported by the National Natural Science Foundation of China (61877031,61462027,61562031) and Science and Technology Project of Jiangxi Education Departmen (GJJ170206).

Abstract: Finding the maximum clique is a well-known NP-complete problem,and the classical algorithms of finding the maximum clique basically use the exact search strategy.Because of the complexity of the NP-complete problem,these algorithms may only be applicable to some special small scale graphs,which are difficult to applied to the complex graphs with large scale vertices and edges.In this paper,aiming at the problem of executing much redundant and ineffective search after finding a maximum clique by using these classical algorithms,this paper proposed a new algorithm based on the partition & recursive and the local-limited search strategy to find a maximum clique in an undirected graph,that is,partitioning a graph into an adjacent sub-graph and suspended sub-graph,then finding recursively the maximum clique of the adjacent sub-graph and that of parts of sub-graph of the suspended sub-graph by setting a search range control function.The experiments in a benchmark data set DIMACS show that this algorithm can find the maximum clique in most of the experimental data,can find the approximate maximum clique in other experimental data that is very close to the maximum clique,and it is much faster than these classical algorithm.Therefore,in many cases with non-precise requirements for the maximum clique,this algorithm has better application value.

CLC Number:

• TP301.6
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