Advertisement

Tight RNC approximations to Max Flow

  • Maria Serna
  • Paul Spirakis
Algorithms I
Part of the Lecture Notes in Computer Science book series (LNCS, volume 480)

Abstract

We show here that the general Maximum Flow problem can be approximated by a RNC algorithm in such a way that for any fixed (or at most polynomially bounded) ε, the absolute performance ratio is at most 1+1/ε. Our results furthermore imply that there is a fully NC approximation scheme for the Maximum Flow problem if and only if there is an algorithm in NC to construct a Maximum Matching in a bipartite graph.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    R. J. Anderson and E. W. Mayr. Approximating P-complete problems. Technical report, Stanford University, 1986.Google Scholar
  2. [2]
    S. A. Cook. A taxonomy of problems with fast parallel algorithms. Information and Control, 64:2–22, 1985.CrossRefGoogle Scholar
  3. [3]
    S. Even. Graph Algorithms. Pitman, London, 1979.Google Scholar
  4. [4]
    M. R. Garey and D. S. Johnson. Computers and Intractability — A Guide to the Theory of NP-Completeness. W. H. Freeman and Co., San Francisco, 1979.Google Scholar
  5. [5]
    L. M. Goldschlager, R. A. Shaw, and J. Staples. The maximum flow problem is log space complete for P. Theoretical Computer Science, 21:105–111, 1982.CrossRefGoogle Scholar
  6. [6]
    D. B. Johnson and S. M. Venkatesan. Parallel algorithms for minimum cuts and maximum flows in planar networks. Journal of the ACM, pages 950–967, 1987.Google Scholar
  7. [7]
    H. J. Karloff. A las Vegas RNC algorithm for maximum matching. Combinatorica, 6:387–392, 1986.Google Scholar
  8. [8]
    R. M. Karp, E. Upfal, and A. Wigderson. Constructing a perfect matching is in Random NC. In 17th Annual ACM Symposium on Theory of Computing, pages 22–32, 1985. Also Combinatorica 6:35–48, 1986.Google Scholar
  9. [9]
    L. Kirousis, M. Serna, and P. Spirakis. The parallel complexity of the subgraph connectivity problem. In 30th Annual IEEE Symposium on Foundations of Computer Science, pages 294–299, 1989.Google Scholar
  10. [10]
    E. L. Lawler. Combinatorial Optimization: Networks and Matroids. Holt, Rinehart and Winston, 1976.Google Scholar
  11. [11]
    K. Mulmuley, U. V. Vazirani, and V. V. Vazirani. Matching is as easy as matrix inversion. In 19th Annual ACM Symposium on Theory of Computing, pages 345–354, 1987.Google Scholar
  12. [12]
    M. Serna and P. Spirakis. The approximability of problems complete for P. In International Symposium on Optimal Algorithms, volume 401 of Lecture Notes in Computer Science, pages 193–204. Springer-Verlag, 1989.Google Scholar
  13. [13]
    M. Serna and P. Spirakis. Applying P-completeness to approximation problems. Technical Report 90.05.14, CTI, Patras University, 1990. Algorithms Review to appear.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Maria Serna
    • 1
  • Paul Spirakis
    • 2
  1. 1.Polytechnic University of CataloniaBarcelonaSpain
  2. 2.Computer Technology InstitutePatras UniversityGreece

Personalised recommendations