Approximation of minimum cost homomorphisms

Abstract

Let H be a fixed graph without loops. We prove that if H is a co-circular arc bigraph then the minimum cost homomorphism problem to H admits a polynomial time constant ratio approximation algorithm; otherwise the minimum cost homomorphism problem to H is known to be not approximable. This solves a problem posed in an earlier paper. For the purposes of the approximation, we provide a new characterization of co-circular arc bigraphs by the existence of min ordering. Our algorithm is then obtained by derandomizing a two-phase randomized procedure. We show a similar result for graphs H in which all vertices have loops: if H is an interval graph, then the minimum cost homomorphism problem to H admits a polynomial time constant ratio approximation algorithm, and otherwise the minimum cost homomorphism problem to H is not approximable. © 2012 Springer-Verlag.