A 27/26-Approximation Algorithm for the Chromatic Sum Coloring of Bipartite Graphs

Authors:
Krzysztof Giaro;Robert Janczewski;Marek Kubale;Michal Malafiejski
Affiliations:
-;-;-;-
Venue:
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Year:
2002

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Abstract

We consider the CHROMATIC SUM PROBLEM on bipartite graphs which appears to be much harder than the classical CHROMATIC NUMBER PROBLEM. We prove that the CHROMATIC SUM PROBLEM is NP-complete on planar bipartite graphs with 驴驴 5, but polynomial on bipartite graphs with 驴驴 3, for which we construct an O(n2)-time algorithm. Hence, we tighten the borderline of intractability for this problem on bipartite graphs with bounded degree, namely: the case 驴 = 3 is easy, 驴 = 5 is hard. Moreover, we construct a 27/26-approximation algorithm for this problem thus improving the best known approximation ratio of 10/9.