Algorithms – ESA 2007

Volume 4698 of the series Lecture Notes in Computer Science pp 522-533

An O(log2 k)-Competitive Algorithm for Metric Bipartite Matching

  • Nikhil BansalAffiliated withIBM T. J. Watson Research Center, Yorktown Heights, NY 10598
  • , Niv BuchbinderAffiliated withComputer Science Department, Technion, Haifa
  • , Anupam GuptaAffiliated withDepartment of Computer Science Carnegie Mellon University
  • , Joseph (Seffi) NaorAffiliated withMicrosoft Research, Redmond, WA. On leave from the CS Dept., Technion, Haifa

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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.