Randomized and approximation algorithms for blue-red matching

Authors:
Christos Nomikos;Aris Pagourtzis;Stathis Zachos
Affiliations:
Department of Computer Science, University of Ioannina;School of Electrical and Computer Engineering, National Technical University of Athens;School of Electrical and Computer Engineering, National Technical University of Athens and CIS Department, Brooklyn College, Cuny
Venue:
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Year:
2007

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Abstract

We introduce the Blue-Red Matching problem: given a graph with red and blue edges, and a bound w, find a maximum matching consisting of at most w edges of each color. We show that Blue-Red Matching is at least as hard as the problem Exact Matching (Papadimitriou and Yannakakis, 1982), for which it is still open whether it can be solved in polynomial time. We present an RNC algorithm for this problem as well as two fast approximation algorithms. We finally show the applicability of our results to the problem of routing and assigning wavelengths to a maximum number of requests in all-optical rings.