A constraint programming approach to the Zahn's decision problem

Abstract

Given a graph G=(S, E), the problem dealt with in this paper consists in partitioning S into a disjoint union of cliques by adding or removing a minimum number z(G) of edges. The problem, which is refered to by the Zahn Problem (ZP), is NP-hard in general. This paper presents a constraint programming approach to ZP. The problem is formulated in terms of a Weighted Constraint Satisfaction Problem (WCSP), a widely used framework for solving hard combinatorial problems. As a seach strategy, we applied a Limited Discrepancy Search coupled with a branch-and-bound algorithm, a combination which has proved to be very advantageous. We compared our approach to a fixed-parameter tractability algorithm, one of the most used algorithms for solving ZP. The comparison clearly show that our approach is very competitive, especially on large ZP instances. © Springer International Publishing Switzerland 2014.