, Volume 6, Issue 4, pp 387–391 | Cite as

A las vegas rnc algorithm for maximum matching

  • Howard J. Karloff


Recently two randomized algorithms were discovered that find a maximum matching in an arbitrary graph in polylog time, when run on a parallel random access machine. Both are Monte Carlo algorithms — they have the drawback that with non-zero probability the output is a non-maximum matching. We use the min-max formula for the size of a maximum matching to convert any Monte Carlo maximum matching algorithm into a Las Vegas (error-free) one. The resulting algorithm returns (with high probability) a maximum matching and a certificate proving that the matching is indeed maximum.

AMS subject classification (1986)

05 C 99 68 E 10 


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  1. [1]
    J. Edmonds, Paths, Trees, and Flowers,Canadian J. Math. 17 (1965), 449–467.MATHMathSciNetGoogle Scholar
  2. [2]
    Z. Galil andV. Pan, Fast and Efficient Randomized Parallel Computation of a Perfect Matching in a Graph,to appear in Proc. of the Twenty-Sixth Annual Symp. on the Foundations of Computer Science, 1985.Google Scholar
  3. [3]
    R. M. Karp, E. Upfal andA. Wigderson, Constructing a perfect matching is in random NC,Combinatorica 6 (1986).Google Scholar
  4. [4]
    R. M. Karp andA. Wigderson, A Fast Parallel Algorithm for the Maximal Independent Set Problem,Proc. of the Sixteenth Ann. ACM Symp. on Theory of Computing (1984), 266–272.Google Scholar
  5. [5]
    L. Lovász,private communication.Google Scholar
  6. [6]
    L. Lovász,Combinatorial Problems and Exercises, North-Holland, New York, 1979.MATHGoogle Scholar
  7. [7]
    L. Lovász, On the Structure of Factorizable Graphs,Acta Mathematica Academiae Scientiarum Hungaricae,23 (1972), 179–195.MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    M. Luby, A Simple Parallel Algorithm for the Maximal Independent Set Problem,Proc. of the Seventeenth Ann. ACM Symp. on Theory of Computing (1985), 1–10.Google Scholar
  9. [9]
    A. Schrijver, Min-max results in combinatorial optimization,in: Mathematical Programming the state of the Art (Bonn 1982), (ed: A. Bachem, M. Grötschel, B. Korte), Springer-Verlag, New York, 1983.Google Scholar

Copyright information

© Akadémiai Kiadó 1986

Authors and Affiliations

  • Howard J. Karloff
    • 1
  1. 1.University of CaliforniaBerkeleyU.S.A.

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