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Jean B. Lasserre (lasserrelaas.fr) 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 halfspace representation of $\Omega$. Keywords: Convex polytope; volume; Laplace transform. Category 1: Combinatorial Optimization (Polyhedra ) Citation: J. of the ACM 48 (2001), 11261140. Download: Entry Submitted: 12/06/2001 Modify/Update this entry  
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