Combinatorica

, Volume 6, Issue 1, pp 35–48 | Cite as

Constructing a perfect matching is in random NC

  • R. M. Karp
  • E. Upfal
  • A. Wigderson
Article

Abstract

We show that the problem of constructing a perfect matching in a graph is in the complexity class Random NC; i.e., the problem is solvable in polylog time by a randomized parallel algorithm using a polynomial-bounded number of processors. We also show that several related problems lie in Random NC. These include:
  1. (i)

    Constructing a perfect matching of maximum weight in a graph whose edge weights are given in unary notation;

     
  2. (ii)

    Constructing a maximum-cardinality matching;

     
  3. (iii)

    Constructing a matching covering a set of vertices of maximum weight in a graph whose vertex weights are given in binary;

     
  4. (iv)

    Constructing a maximums-t flow in a directed graph whose edge weights are given in unary.

     

AMS subject classification (1980)

68 E 10 

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Copyright information

© Akadémiai Kiadó 1986

Authors and Affiliations

  • R. M. Karp
    • 1
  • E. Upfal
    • 2
  • A. Wigderson
    • 3
  1. 1.Comp. Sci. DivisionUniversity of CaliforniaBerkeleyUSA
  2. 2.Comp. Sci. DepartmentStanford UniversityStanfordUSA
  3. 3.IBM San Jose Res. Lab.San JoseUSA

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