Faster Branch and Bound Algorithms for Solving the Maximum Clique Problem

We present efficient branch and bound algorithms for solving the Maximum Clique Problem. First strategy is to store the size of clique consisting of a seed vertex in a subset induced by candidate set of the seed vertex. Results stored are further used to reduce the computation involved in computing clique consisting of other seed vertices in another subset of the graph. This approach along with greedy algorithm for graph coloring, reduce the search space but does not always outperform the first strategy due to overhead involved in computing the graph coloring. Experiments on DIMACS benchmarks and random graphs demonstrate that the improved branch and bound algorithms are faster than the original algorithm by Carraghan and Pardalos [7]. Keywords— Clique, Branch and Bound Algorithm, Maximum Clique Problem, Greedy algorithm, Graph Coloring