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An Almost Linear Time Approximation Algorithm for the Permanent of a Random (0-1) Matrix

  • Martin Fürer
  • Shiva Prasad Kasiviswanathan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3328)

Abstract

We present a simple randomized algorithm for approximating permanents. The algorithm with inputs A, ε> 0 produces an output X A with (1 − ε)per(A) ≤ X A  ≤ (1 + ε) per (A) for almost all (0-1) matrices A. For any positive constant ε > 0 , and almost all (0-1) matrices the algorithm runs in time O(n 2 ω), i.e., almost linear in the size of the matrix, where ω = ω(n) is any function satisfying ω(n) → ∞ as n → ∞. This improves the previous bound of O(n 3 ω) for such matrices. The estimator can also be used to estimate the size of a backtrack tree.

Keywords

Random Matrix Unbiased Estimator Random Graph Model Polynomial Time Deterministic Algorithm Polynomial Time Turing Machine 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Martin Fürer
    • 1
  • Shiva Prasad Kasiviswanathan
    • 1
  1. 1.Computer Science and EngineeringPennsylvania State UniversityUniversity Park

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