On the approximability of the Max Edge-Coloring problem

Giorgio Lucarelli (1) , Ioannis Milis (2)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
2 CS-AUEB - Department of Informatics [Athens]

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 edges in each color class. This problem arises in optical communication systems and has been well studied during last years. However, no algorithm of approximation ratio 2 − δ, for any constant δ > 0, is known for general or bipartite graphs, while the complexity of the problem on trees remains an open question. In this paper we present new approximation results towards these questions. In fact, 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.

Domaines: Algorithme et structure de données [cs.DS]; Complexité [cs.CC]; Recherche opérationnelle [math.OC]

Giorgio Lucarelli, Ioannis Milis. On the approximability of the Max Edge-Coloring problem. 2010. ⟨hal-00876861⟩