The exact computation of the permanent of a matrix is #P-complete. Many efforts have been made to efficiently approximate the permanent. In this talk we will survey some of these methods, both probabilistic and deterministic.

The papers below and the references within them serve as a good source of information on this topic.


  1. 1.
    Barvinok, A.I.: Computing Mixed Discriminants, Mixed Volumes, and Perma- nents. Discrete & Computational Geometry 18, 205–237 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Dagum, P., Luby, M.: Approximating the Permanent of Graphs with Large Factors. Theretical Computer Science Part A 102, 283–305 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Feige, U., Lund, C.: On the hardness of computing the permanent of random matrices. STOC 24, 643–654 (1992)Google Scholar
  4. 4.
    Jerrum, M., Sinclair, A.: Approximating the permanent. SIAM J. Comput. 18, 1149–1178 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Jerrum, M., Vazirani, U.: A mildly exponential approximation algorithm for the permanent. Algorithmica 16(4/5), 392–401 (1996)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Kasteleyn, P.W.: The statistics of dimers on a lattice 1. The number of dimmer arrangements on a quadratic lattice. Physica 27, 1209–1225 (1961)CrossRefGoogle Scholar
  7. 7.
    Karmarkar, N., Karp, R., Lipton, R., Lovasz, L., Luby, M.: A Monte-Carlo algorithm for estimating the permanent. SIAM Journal on Computing 22(2), 284–293 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Valiant, L.G.: The complexity of computing the permanent. Theoretical Computer Science 8(2), 189–201 (1979)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Avi Wigderson
    • 1
    • 2
  1. 1.The Hebrew UniversityJerusalem
  2. 2.The Institute for Advanced StudyPrinceton

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