On the max-weight edge coloring problem

Authors:
Giorgio Lucarelli;Ioannis Milis;Vangelis T. Paschos
Affiliations:
Department of Informatics, Athens University of Economics and Business, Athens, Greece 10434;Department of Informatics, Athens University of Economics and Business, Athens, Greece 10434;LAMSADE, CNRS UMR 7024 and Université Paris-Dauphine, Paris, France 75016
Venue:
Journal of Combinatorial Optimization
Year:
2010

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Abstract

We study the following generalization of the classical edge coloring problem: Given a weighted graph, find a partition of its edges into matchings (colors), each one of weight equal to the maximum weight of its edges, so that the total weight of the partition is minimized. We explore the frontier between polynomial and NP-hard variants of the problem, with respect to the class of the underlying graph, as well as the approximability of NP-hard variants. In particular, we present polynomial algorithms for bounded degree trees and star of chains, as well as an approximation algorithm for bipartite graphs of maximum degree at most twelve which beats the best known approximation ratios.