**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30054

##### A New Effective Local Search Heuristic for the Maximum Clique Problem

**Authors:**
S. Balaji

**Abstract:**

An edge based local search algorithm, called ELS, is proposed for the maximum clique problem (MCP), a well-known combinatorial optimization problem. ELS is a two phased local search method effectively £nds the near optimal solutions for the MCP. A parameter ’support’ of vertices de£ned in the ELS greatly reduces the more number of random selections among vertices and also the number of iterations and running times. Computational results on BHOSLIB and DIMACS benchmark graphs indicate that ELS is capable of achieving state-of-the-art-performance for the maximum clique with reasonable average running times.

**Keywords:**
Maximum clique,
local search,
heuristic,
NP-complete.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1087856

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