An almost linear time approximation algorithm for the permanent of a random (0-1) matrix

Martin Fürer, Shiva Prasad Kasiviswanathan

    Research output: Contribution to journalArticle

    4 Scopus citations

    Abstract

    We present a simple randomized algorithm for approximating permanents. The algorithm with inputs A, ∈ > 0 produces an output XA with (1 - ∈)per(A) ≤ XA ≤ (1 + ∈)per(A) for almost all (0-1) matrices A. For any positive constant ∈ > 0, and almost all (0-1) matrices the algorithm runs in time O(n2ω), 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(n3ω) for such matrices. The estimator can also be used to estimate the size of a backtrack tree.

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

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