Approximation algorithms for maximum edge coloring problem

Abstract

We propose polynomial time approximation algorithms for a novel maximum edge coloring problem which arises from the field of wireless mesh networks [8]. The problem is about coloring all the edges in a graph and finding a coloring solution which uses the maximum number of colors with the constraint, for every vertex in the graph, all the edges incident to it are colored with no more than q(q ∈ ℤ, q > 2) colors. The case q = 2 is of great importance in practice. In this paper, we design approximation algorithms for cases q = 2 and q > 2 with approximation ratio 2.5 and 1 + 4q-2/3q2-5q+2 respectively. The algorithms can give practically usable estimations on the upper bounds of the numbers of the channels used in wireless mesh networks. © Springer-Verlag Berlin Heidelberg 2007.