Reusing the same coloring in the child nodes of the search tree for the maximum clique problem

Abstract

In this paper we present a new approach to reduce the computational time spent on coloring in one of the recent branch-and-bound algorithms for the maximum clique problem. In this algorithm candidates to the maximum clique are colored in every search tree node. We suggest that the coloring computed in the parent node is reused for the child nodes when it does not lead to many new branches. So we reuse the same coloring only in the nodes for which the upper bound is greater than the current best solution only by a small value δ. The obtained increase in performance reaches 70% on benchmark instances.