A new algorithm for the volume of a convex polytope

Abstract

We provide two algorithms for computing the volume of a convex polytope with half-space representation {x>=0; Ax <=b} for some (m,n) matrix A and some m-vector b. Both algorithms have a O(n^m) computational complexity which makes them especially attractive for large n and relatively small m when the other methods with O(m^n) complexity fail. The methodology which differs from previous existing methods uses a Laplace transform technique that is well-suited to the half-space representation of the polytope.