An Almost Linear Time Approximation Algorithm for the Permanent of a Random (0-1) Matrix
We present a simple randomized algorithm for approximating permanents. The algorithm with inputs A, ε> 0 produces an output XA with (1 − ε)per(A) ≤ XA ≤ (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...
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| Veröffentlicht in: | FSTTCS 2004: Foundations of Software Technology and Theoretical Computer Science 2004-01, p.263-274 |
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| container_title | FSTTCS 2004: Foundations of Software Technology and Theoretical Computer Science |
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| creator | Fürer, Martin Kasiviswanathan, Shiva Prasad |
| description | We present a simple randomized algorithm for approximating permanents. The algorithm with inputs A, ε> 0 produces an output XA with (1 − ε)per(A) ≤ XA ≤ (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(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. |
| doi_str_mv | 10.1007/978-3-540-30538-5_22 |
| format | Article |
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| subjects | Applied sciences Computer science control theory systems Exact sciences and technology Polynomial Time Deterministic Algorithm Polynomial Time Turing Machine Random Graph Model Random Matrix Theoretical computing Unbiased Estimator |
| title | An Almost Linear Time Approximation Algorithm for the Permanent of a Random (0-1) Matrix |
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