Bit arrays from row and column sums

Abstract

A number of fields, especially within ecology, use bit arrays (i.e. matrices with entries either 0 or 1) to study distributions. In particular such an array serves as a presence/absence array to describe the distribution of species (a given row) across islands (a given column). In such an environment one concept is that the total number of species on a given island will stay fixed, as will the total number of islands populated by a given species. Thus a primary constraint is fixed row/column sums.Now we need to create sample bit-matrices that meet these row and column sum constraints. If such matrices are 'properly random' then conclusions are drawn about the actual physical solution. It is not our intent to consider such conclusions, but rather to discuss only the possible ways to generate such bit-matrices and describe a new algorithm for generation.