## 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(log^{2} k) competitive randomized algorithm for the problem. This improves upon the best known guarantee of O(log^{3} 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 In k.

Original language | English |
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Title of host publication | Algorithms - ESA 2007 - 15th Annual European Symposium, Proceedings |

Publisher | Springer Verlag |

Pages | 522-533 |

Number of pages | 12 |

ISBN (Print) | 9783540755197 |

DOIs | |

State | Published - 2007 |

Externally published | Yes |

Event | 15th Annual European Symposium on Algorithms, ESA 2007 - Eilat, Israel Duration: 8 Oct 2007 → 10 Oct 2007 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 4698 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 15th Annual European Symposium on Algorithms, ESA 2007 |
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Country/Territory | Israel |

City | Eilat |

Period | 8/10/07 → 10/10/07 |

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