The Distance Approach to Approximate Combinatorial Counting
Combinatorics
2007-05-23 v1 Metric Geometry
Abstract
We develop general methods to obtain fast (polynomial time) estimates of the cardinality of a combinatorially defined set via solving some randomly generated optimization problems on the set. Geometrically, we estimate the cardinality of a subset of the Boolean cube via the average distance from a point in the cube to the subset. As an application, we present a new randomized polynomial time algorithm which approximates the permanent of a 0-1 matrix by solving a small number of Assignment problems.
Cite
@article{arxiv.math/0005263,
title = {The Distance Approach to Approximate Combinatorial Counting},
author = {Alexander Barvinok and Alex Samorodnitsky},
journal= {arXiv preprint arXiv:math/0005263},
year = {2007}
}
Comments
34 pages