Approximation algorithms for bounded color matchings via convex decompositions

Abstract

We study the following generalization of the maximum matching problem in general graphs: Given a simple non-directed graph G=(V,E) and a partition of the edges into k classes (i.e. E=E 1∩⋯∩E k ), we would like to compute a matching M on G of maximum cardinality or profit, such that |M∩E j |≤wbj for every class Eb j. Such problems were first studied in the context of network design in [17]. We study the problem from a linear programming point of view: We provide a polynomial time -approximation algorithm for the weighted case, matching the integrality gap of the natural LP formulation of the problem. For this, we use and adapt the technique of approximate convex decompositions [19] together with a different analysis and a polyhedral characterization of the natural linear program to derive our result. This improves over the existing, but with additive violation of the color bounds, approximation algorithm [14]. © 2014 Springer-Verlag Berlin Heidelberg.