  We present a computational approach for generating Markov bases for multi-way
contingency tables whose cells counts might be constrained by fixed marginals
and by lower and upper bounds. Our framework includes tables with structural
zeros as a particular case. In- stead of computing the entire Markov basis in
an initial step, our framework finds sets of local moves that connect each
table in the reference set with a set of neighbor tables. We construct a Markov
chain on the reference set of tables that requires only a set of local moves at
each iteration. The union of these sets of local moves forms a dynamic Markov
basis. We illustrate the practicality of our algorithms in the estimation of
exact p-values for a three-way table with structural zeros and a sparse
eight-way table. Computer code implementing the methods de- scribed in the
article as well as the two datasets used in the numerical examples are
available as supplemental material.
