The Distance Approach to Approximate Combinatorial Counting [article]

Alexander Barvinok, Alex Samorodnitsky
2000 arXiv   pre-print
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.
arXiv:math/0005263v1 fatcat:2z4jliry3jcedhrcjwb2dmpwgq