Theory of linear and integer programming
Theory of linear and integer programming
On the complexity of computing the volume of a polyhedron
SIAM Journal on Computing
Two Algorithms for Determining Volumes of Convex Polyhedra
Journal of the ACM (JACM)
Cost-based labeling of groups of mass spectra
SIGMOD '04 Proceedings of the 2004 ACM SIGMOD international conference on Management of data
ACM SIGGRAPH 2005 Papers
Multivariate splines and polytopes
Journal of Approximation Theory
Time-bounded verification of CTMCs against real-time specifications
FORMATS'11 Proceedings of the 9th international conference on Formal modeling and analysis of timed systems
Verification of linear duration properties over continuous-time markov chains
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Discrete Optimization
Solving the knapsack problem via Z-transform
Operations Research Letters
Verification of linear duration properties over continuous-time markov chains
ACM Transactions on Computational Logic (TOCL)
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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.