A Dynamic Programming Approach for Approximate Uniform Generation of Binary Matrices with Specified Margins

Consider the collection of all binary matrices having a specific sequence of row and column sums and consider sampling binary matrices uniformly from this collection. Practical algorithms for exact uniform sampling are not known, but there are practical algorithms for approximate uniform sampling. Here it is shown how dynamic programming and recent asymptotic enumeration results can be used to simplify and improve a certain class of approximate uniform samplers. The dynamic programming perspective suggests interesting generalizations.