Infra-chromatic bound for exact maximum clique search. (December 2015) - San Segundo, Pablo; Nikolaev, Alexey; Batsyn, Mikhail
Abstract: Many efficient exact branch and bound maximum clique solvers use approximate coloring to compute an upper bound on the clique number for every subproblem. This technique reasonably promises tight bounds on average, but never tighter than the chromatic number of the graph. Li and Quan, 2010, AAAI Conference, p. 128–133 describe a way to compute even tighter bounds by reducing each colored subproblem to maximum satisfiability problem (MaxSAT). Moreover they show empirically that the new bounds obtained may be lower than the chromatic number. Based on this idea this paper shows an efficient way to compute related "infra-chromatic" upper bounds without an explicit MaxSAT encoding. The reported results show some of the best times for a stand-alone computer over a number of instances from standard benchmarks. Highlights: New state-of-the-art exact maximum clique approximate color algorithm. Improved bounds possibly below the chromatic number.