research-article

Linear-Time Approximation for Maximum Weight Matching

Authors:

Seth PettieAuthors Info & Claims

Journal of the ACM (JACM), Volume 61, Issue 1

Article No.: 1, Pages 1 - 23

https://doi.org/10.1145/2529989

Published: 01 January 2014 Publication History

Abstract

The maximum cardinality and maximum weight matching problems can be solved in Õ(m√n) time, a bound that has resisted improvement despite decades of research. (Here m and n are the number of edges and vertices.) In this article, we demonstrate that this “m√n barrier” can be bypassed by approximation. For any ε > 0, we give an algorithm that computes a (1 − ε)-approximate maximum weight matching in O(mε⁻¹ log ε⁻¹) time, that is, optimal linear time for any fixed ε. Our algorithm is dramatically simpler than the best exact maximum weight matching algorithms on general graphs and should be appealing in all applications that can tolerate a negligible relative error.

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Index Terms

Linear-Time Approximation for Maximum Weight Matching
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms

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cover image Journal of the ACM

Journal of the ACM Volume 61, Issue 1

January 2014

222 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/2578041

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Published: 01 January 2014

Accepted: 01 September 2013

Revised: 01 September 2013

Received: 01 December 2011

Published in JACM Volume 61, Issue 1

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