A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries

2001/07/06 by Mark Jerrum, Alistair Sinclair, Eric Vigoda · 1 citation
Computer Science · Mathematics · #Matrix Theory and Algorithms #Advanced Optimization Algorithms Research #Polynomial and algebraic computation #Algorithm #Matrix polynomial #Matrix (chemical analysis) #Time complexity #Mathematics #Polynomial #Polynomial matrix #Computer science #Combinatorics #Mathematical analysis

paper · doi:10.1145/1008731.1008738

openalex publication_date 2001/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/15

Abstract

We present a polynomial-time randomized algorithm for estimating the permanent of an arbitrary n × n matrix with nonnegative entries. This algorithm---technically a "fully-polynomial randomized approximation scheme"---computes an approximation that is, with high probability, within arbitrarily small specified relative error of the true value of the permanent.

Citations

• The complexity of computing the permanent
• A Chernoff Bound for Random Walks on Expander Graphs

Cited by

• Permanent (mathematics) [wikipedia]