### Abstract

We present a simple randomized algorithm for approximating permanents. The algorithm with inputs A, ∈ > 0 produces an output XA with (1 - ∈)per(A) ≤ X_{A} ≤ (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(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.

Original language | English (US) |
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Pages (from-to) | 263-274 |

Number of pages | 12 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 3328 |

DOIs | |

State | Published - Jan 1 2004 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Fürer, M., & Kasiviswanathan, S. P. (2004). An almost linear time approximation algorithm for the permanent of a random (0-1) matrix.

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*,*3328*, 263-274. https://doi.org/10.1007/978-3-540-30538-5_22