The probabilistic minimum coloring problem. (Extended Abstract)

Abstract

We study the probabilistic coloring problem (PCOLOR.) under a modification strategy consisting, given an a priori solution C, of removing the absent vertices from C. We compute the objective function associated with this strategy, we give bounds on its value, we characterize the complexity of computing it and the one of computing the optimal solution associated with. We show that PCOLOR is NP-hard and design a polynomial time approximation algorithm achieving non-trivial approximation ratio. We then show that probabilistic coloring remains NP-hard even in bipartite graphs and that the unique 2-coloring in such graphs is a constant ratio approximation. We finally prove that PCOLOR is polynomial when dealing with complements of bipartite graphs. © Springer-Verlag Berlin Heidelberg 2003.