A Laplace transform algorithm for the volume of a convex polytope. - Lasserre, Jean B. (Journal of the ACM)
We provide two algorithms for computing the volume of the convex polytope Ω : = {x ∈ ℝn+ | Ax ≤ b}, for A, ∈ ℝm×n, b ∈ ℝn. The computational complexity of both algorithms is essentially described by nm, which makes them especially attractive for large n and relatively small m, when the other methods with O(mn) 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 Ω.