An O(log2k)-competitive algorithm for metric bipartite matching

Authors:
Nikhil Bansal;Niv Buchbinder;Anupam Gupta;Joseph Seffi Naor
Affiliations:
IBM T. J. Watson Research Center, Yorktown Heights, NY;Computer Science Department, Technion, Haifa, Israel;Department of Computer Science Carnegie Mellon University;Microsoft Research, Redmond, WA
Venue:
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Year:
2007

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Abstract

We consider the online metric matching problem. In this problem, we are given a graph with edge weights satisfying the triangle inequality, and k vertices that are designated as the right side of the matching. Over time up to k requests arrive at an arbitrary subset of vertices in the graph and each vertex must be matched to a right side vertex immediately upon arrival. A vertex cannot be rematched to another vertex once it is matched. The goal is to minimize the total weight of the matching. We give a O(log2 k) competitive randomized algorithm for the problem. This improves upon the best known guarantee of O(log3 k) due to Meyerson, Nanavati and Poplawski [19]. It is well known that no deterministic algorithm can have a competitive less than 2k - 1, and that no randomized algorithm can have a competitive ratio of less than ln k.