- A Laplace transform algorithm for the volume of a convex polytope Jean B. Lasserre (lasserrelaas.fr) Eduardo S. Zeron (eszeronmath.cinvestav.mx) Abstract: We provide two algorithms for computing the volume of the convex polytope $\Omega:=\{x\in \R^n_+ \,|\,Ax\leq b\}$, for $A\in\R^{m\times n}, b\in\R^n$. The computational complexity of both algorithms is essentially described by $n^m$, 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 $\Omega$. Keywords: Convex polytope; volume; Laplace transform. Category 1: Combinatorial Optimization (Polyhedra ) Citation: J. of the ACM 48 (2001), 1126--1140. Download: Entry Submitted: 12/06/2001Entry Accepted: 12/06/2001Entry Last Modified: 07/13/2002Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.