A randomized algorithm for finding a near-maximum clique and its experimental evaluations

The so-called Maximum Clique Problem is one of the most famous NP-complete problems for which it is difficult to find a solution. Given an indirected graph, we present here a polynomial-time randomized algorithm RaCLIQUE for finding a near-maximum clique. While the basic idea of the algorithm comes from Boltzmann machines, it employs no simulated annealing at all and hence it is simple to control its execution. We have confirmed in experiments for several random and nonrandom graphs with up to 400 nodes that very good solutions can be found efficiently compared with the other conventional algorithms.