Precise polynomial heuristic for an NP-complete problem

Abstract

We introduce a simple, efficient and precise polynomial heuristic for a key NP complete problem, minimum vertex cover. Our method is iterative and operates in probability space. Once a stable probability solution is found we find the true combinatorial solution from the probabilities. For system sizes which are amenable to exact solution by conventional means, we find a correct minimum vertex cover for all cases which we have tested, which include random graphs and diluted triangular lattices of up to 100 sites. We present precise data for minimum vertex cover on graphs of up to 50,000 sites. Extensions of the method to hard core lattices gases and other NP problems are discussed.