A new algorithm for the volume of a convex polytope
J. B. Lasserre, E. S. Zeron
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(nm) computational complexity 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 the polytope.
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