Approximation Algorithms for the Max-coloring Problem

Given a graph G = (V, E) and positive integral vertex weights w : V → N, the max-coloring problem seeks to find a proper vertex coloring of G whose color classes C1, C2, . . . , Ck, minimize k i=1 maxv∈Ci w(v). The problem arises in scheduling conflicting jobs in batches and in minimizing buffer size in dedicated memory managers. In this paper we present three approximation algorithms and one inapproximability result for the max-coloring problem. We show that if for a class of graphs G, the classical problem of finding a proper vertex coloring with fewest colors has a c-approximation, then for that class G of graphs, max-coloring has a 4c-approximation algorithm. As a consequence, we obtain a 4-approximation algorithm to solve max-coloring on perfect graphs, and well-known subclasses such as chordal graphs, and permutation graphs. We also obtain constant-factor algorithms for maxcoloring on classes of graphs such as circle graphs, circular arc graphs, and unit disk graphs, whic...

• Type: Conference
• Year: 2005
• Where: ICALP
• Authors: Sriram V. Pemmaraju, Rajiv Raman
• Keywords: Approximation Algorithm, Bipartite Graphs, ICALP 2005, Proper Vertex Coloring, Theoretical Computer Science