Volume 25 (2017) Pages 667-677
We present further improvements to a branch-and-bound maximum-clique-finding algorithm MCS (WALCOM 2010, LNCS 5942, pp.191-203) that was shown to be fast. First, we employ a variant of an efficient approximation algorithm KLS for finding a maximum clique. Second, we make use of appropriate sorting of vertices only near the root of the search tree. Third, we employ a lightened approximate coloring mainly near the leaves of the search tree. A new algorithm obtained from MCS with the above improvements is named k5_MCT. It is shown that k5_MCT is much faster than MCS by extensive computational experiments. In particular, k5_MCT is shown to be faster than MCS for gen400_p0.9_75, gen400_p0.9_65 and gen400_p0.9_55 by over 81,000, 39,000 and 19,000 times, respectively.