# A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries

@article{Jerrum2004APA, title={A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries}, author={M. Jerrum and A. Sinclair and Eric Vigoda}, journal={J. ACM}, year={2004}, volume={51}, pages={671-697} }

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.

#### Paper Mentions

#### 652 Citations

A remark on approximating permanents of positive definite matrices.

- Mathematics, Computer Science
- 2020

Simply Exponential Approximation of the Permanent of Positive Semidefinite Matrices

- Computer Science, Mathematics
- 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)
- 2017

A Tight Analysis of Bethe Approximation for Permanent

- Mathematics, Computer Science
- 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)
- 2019

A deterministic approximation algorithm for computing the permanent of a 0, 1 matrix

- Computer Science, Mathematics
- J. Comput. Syst. Sci.
- 2010

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

- Computer Science, Mathematics
- FSTTCS
- 2004

A Note on Deterministic Poly-Time Algorithms for Partition Functions Associated with Boolean Matrices with Prescribed Row and Column Sums

- Mathematics, Computer Science
- MFCS
- 2013

A polynomial-time approximation algorithm for the number of k-matchings in bipartite graphs

- Computer Science, Mathematics
- ArXiv
- 2006

Boolean matrices with prescribed row/column sums and stable homogeneous polynomials: Combinatorial and algorithmic applications

- Computer Science, Mathematics
- Inf. Comput.
- 2013

Approximating the Permanent of a Random Matrix with Vanishing Mean

- Mathematics, Computer Science
- 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)
- 2018