Combining Efficient Preprocessing and Incremental MaxSAT Reasoning for MaxClique in Large Graphs

We describe a new exact algorithm for MaxClique, called LMC (short for Large MaxClique), that is especially suited for large sparse graphs. LMC is competitive because it combines an efficient preprocessing procedure and incremental MaxSAT reasoning in a branch-and-bound scheme. The empirical results show that LMC outperforms existing exact MaxClique algorithms on large sparse graphs from real-world applications. © 2016 The Authors and IOS Press.This article is published online with Open Access by IOS Press and distributed under the terms of the Creative Commons Attribution Non-Commercial License 4.0 (CC BY-NC 4.0).This work is supported by NSFC Grant No. 61370184, No. 61272014, and No. 61472147. The third author was supported by Mobility Grant PRX16/00215 of the Ministerio de Educacion, Cultura y Deporte, the Generalitat de Catalunya grant AGAUR 2014-SGR-118, and the MINECO-FEDER project RASO TIN2015-71799-C2-1-P.Peer Reviewe