Given a polyhedron P by a list of inequalities we develop unbiased estimates of the number of vertices and bases of P. The estimates are based on applying tree estimation methods to the reverse search technique. The time to generate an unbiased estimate is essentially bounded by the time taken to solve a linear program on P with the simplex method. Computational experience is reported. The method can be applied to estimate the output size of other enumeration problems solvable by reverse search.
['David Avis', 'Luc Devroye']
Estimating the number of vertices of a polyhedron