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

@article{Jerrum2001APA, title={A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries}, author={Mark Jerrum and Alistair Sinclair and Eric Vigoda}, journal={Electron. Colloquium Comput. Complex.}, year={2001}, volume={TR00} }

We present a fully-polynomial randomized approximation scheme for computing the permanent of an arbitrary matrix with non-negative entries.

## 262 Citations

### An asymptotic approximation for the permanent of a doubly stochastic matrix

- Mathematics
- 2012

A determinantal approximation is obtained for the permanent of a doubly stochastic matrix. For moderate-deviation matrix sequences, the asymptotic relative error is of order O(n−1).

### FPRAS for computing a lower bound for weighted matching polynomial of graphs

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We give a fully polynomial randomized approximation scheme to compute a lower bound for the matching polynomial of any weighted graph at a positive argument. For the matching polynomial of complete…

### Probability and Computation

- Mathematics2011 Second International Conference on Networking and Computing
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This note reviews some randomized algorithms which the author has been concerned with, having been motivated by the above question.

### Random path method with pivoting for computing permanents of matrices

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

- MathematicsArXiv
- 2006

We show that the number of k-matching in a given undirected graph G is equal to the number of perfect matching of the corresponding graph Gk on an even number of vertices divided by a suitable…

### Approximating the Permanent in O ∗ ( n 7 ) Time

- Computer Science
- 2004

The first polynomial-time algorithm to approximate (with arbitrary precision) the permanent of a non-negative matrix was presented by Jerrum, Sinclair and Vigoda, and a O∗(n7) time algorithm is presented.

### A Deterministic Algorithm for Approximating the Mixed Discriminant and Mixed Volume, and a Combinatorial Corollary

- Mathematics, Computer ScienceDiscret. Comput. Geom.
- 2002

We present a deterministic polynomial-time algorithm that computes the mixed discriminant of an n -tuple of positive semidefinite matrices to within an exponential multiplicative factor. To this end…

### Solving convex programs by random walks

- Mathematics, Computer ScienceJACM
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A simple new algorithm for convex optimization based on sampling by a random walk is presented, which extends naturally to minimizing quasi-convex functions and to other generalizations.

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

- Computer Science, MathematicsFSTTCS
- 2004

The algorithm with inputs A, ∈ > 0 produces an output X A with (1-∈)per(A) 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.

### On the algebraic complexity of some families of coloured Tutte polynomials

- MathematicsAdv. Appl. Math.
- 2004

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