, Volume 7, Issue 1, pp 105–113

Matching is as easy as matrix inversion

  • Ketan Mulmuley
  • Umesh V. Vazirani
  • Vijay V. Vazirani

DOI: 10.1007/BF02579206

Cite this article as:
Mulmuley, K., Vazirani, U.V. & Vazirani, V.V. Combinatorica (1987) 7: 105. doi:10.1007/BF02579206


We present a new algorithm for finding a maximum matching in a general graph. The special feature of our algorithm is that its only computationally non-trivial step is the inversion of a single integer matrix. Since this step can be parallelized, we get a simple parallel (RNC2) algorithm. At the heart of our algorithm lies a probabilistic lemma, the isolating lemma. We show other applications of this lemma to parallel computation and randomized reductions.

AMS subject classification (1980)

68 E 1005 C 25

Copyright information

© Akadémiai Kiadó 1987

Authors and Affiliations

  • Ketan Mulmuley
    • 1
  • Umesh V. Vazirani
    • 2
  • Vijay V. Vazirani
    • 3
  1. 1.Comp. Sci. Dept.University of CaliforniaBerkeleyUSA
  2. 2.MSRIBerkeleyUSA
  3. 3.Comp. Sci. Dept.Cornell UniversityIthacaUSA