Autor(es)

Flavia Bonomo and Gianpaolo Oriolo and Claudia Snels and Gautier Stauffer

URL Pública

Abstract

We give new algorithms for the minimum (weighted) clique cover in a claw-free perfect graph G, improving the complexity from O(|V(G)|5) to O(|V(G)|3). The new algorithms build upon neat reformulations of the problem: it basically reduces either to solving a 2-SAT instance (in the unweighted case) or to testing if a polyhedra associated with the edge-vertex incidence matrix of a bidirected graph has an integer solution (in the weighted case). The latter question was elegantly answered using neat polyhedral arguments by Schrijver in 1994. We give an alternative approach to this question combining pure combinatorial arguments (using techniques from 2-SAT and shortest paths) with polyhedral ones. Our approach is inspired by an algorithm from the Constraint Logic Programming community and we give as a side benefit a formal proof that the corresponding algorithm is correct (apparently answering an open …