A local core number based algorithm for the maximum clique problem

Document Type : Research Paper

Authors

Department of computer science, University of Shahrekord, Shahrekord, Iran

Abstract

‎The maximum clique problem (MCP) is to determine a complete subgraph of maximum cardinality in a graph‎. ‎MCP is a fundamental problem in combinatorial optimization and is noticeable for its wide range of applications‎. ‎In this paper‎, ‎we present two branch-and-bound exact algorithms for finding a maximum clique in an undirected graph‎. ‎Many efficient exact branch and bound maximum clique algorithms use approximate coloring to compute an upper bound on the clique number but‎, ‎as a new pruning strategy‎, ‎we show that local core number is more efficient‎. ‎Moreover‎, ‎instead of neighbors set of a vertex‎, ‎our search area is restricted to a subset of the set in each subproblem which speeds up clique finding process‎. ‎This subset is based on the core of the vertices of a given graph‎. ‎We improved the MCQ and MaxCliqueDyn algorithms with respect to the new pruning strategy and search area restriction‎. ‎Experimental results demonstrate that the improved algorithms outperform the previous well-known algorithms for many instances when applied to DIMACS benchmark and random graphs‎.

Keywords

Main Subjects


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Volume 10, Issue 3 - Serial Number 3
September 2021
Pages 149-163
  • Receive Date: 24 November 2019
  • Revise Date: 30 September 2020
  • Accept Date: 21 January 2021
  • Published Online: 01 September 2021