Improved approximation algorithms for the max-edge coloring problem

Authors:
Giorgio Lucarelli;Ioannis Milis
Affiliations:
LAMSADE, Université Paris-Dauphine and CNRS;Department of Informatics, Athens University of Economics and Business
Venue:
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
Year:
2011

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Abstract

The max edge-coloring problem asks for a proper edge-coloring of an edge-weighted graph minimizing the sum of the weights of the heaviest edge in each color class. In this paper we present a PTAS for trees and an 1.74-approximation algorithm for bipartite graphs; we also adapt the last algorithm to one for general graphs of the same, asymptotically, approximation ratio. Up to now, no approximation algorithm of ratio 2-δ, for any constant δ 0, was known for general or bipartite graphs, while the complexity of the problem on trees remains an open question.