Exact Enumeration and Sampling of Matrices with Specified Margins

TL;DR

This paper introduces a dynamic programming algorithm for exact enumeration and uniform sampling of matrices with fixed margins, applicable to large, non-regular matrices with bounded column sums, enabling precise combinatorial analysis.

Contribution

It presents a polynomial-time algorithm for exact counting and sampling of matrices with specified margins, extending applicability to non-regular and large matrices.

Findings

Efficient polynomial-time algorithm for matrices with bounded column sums.

Applicable to non-regular margins and large matrices.

Enables exact uniform sampling of matrices.

Abstract

We describe a dynamic programming algorithm for exact counting and exact uniform sampling of matrices with specified row and column sums. The algorithm runs in polynomial time when the column sums are bounded. Binary or non-negative integer matrices are handled. The method is distinguished by applicability to non-regular margins, tractability on large matrices, and the capacity for exact sampling.