An O(log2k)-Competitive Algorithm for Metric Bipartite Matching

  • Nikhil Bansal
  • Niv Buchbinder
  • Anupam Gupta
  • Joseph (Seffi) Naor
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4698)

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(log2k) competitive randomized algorithm for the problem. This improves upon the best known guarantee of O(log3k) 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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Nikhil Bansal
    • 1
  • Niv Buchbinder
    • 2
  • Anupam Gupta
    • 3
  • Joseph (Seffi) Naor
    • 4
  1. 1.IBM T. J. Watson Research Center, Yorktown Heights, NY 10598 
  2. 2.Computer Science Department, Technion, HaifaIsrael
  3. 3.Department of Computer Science Carnegie Mellon University 
  4. 4.Microsoft Research, Redmond, WA. On leave from the CS Dept., Technion, HaifaIsrael

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