Abstract
In this paper we present improvements to one of the most recent and fastest branch-and-bound algorithm for the maximum clique problem--MCS algorithm by Tomita et al. (Proceedings of the 4th international conference on Algorithms and Computation, WALCOM'10, pp. 191---203, 2010). The suggested improvements include: incorporating of an efficient heuristic returning a high-quality initial solution, fast detection of clique vertices in a set of candidates, better initial colouring, and avoiding dynamic memory allocation. Our computational study shows some impressive results, mainly we have solved p_hat1000-3 benchmark instance which is intractable for MCS algorithm and got speedups of 7, 3000, and 13000 times for gen400_p0.9_55, gen400_p0.9_65, and gen400_p0.9_75 instances correspondingly.
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