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Journal Articles ACM Transactions on Mathematical Software Year : 2018

Efficient Random-Walk Methods for Approximating Polytope Volume

Practical Polytope Volume Approximation

Abstract

We experimentally study the fundamental problem of computing the volume of a convex polytope given as an intersection of linear inequalities. We implement and evaluate practical randomized algorithms for accurately approximating the polytope's volume in high dimensions (e.g. one hundred). To carry out this efficiently we experimentally correlate the effect of parameters, such as random walk length and number of sample points, on accuracy and runtime. Moreover, we exploit the problem's geometry by implementing an iterative rounding procedure, computing partial generations of random points and designing fast polytope boundary oracles. Our publicly available code is significantly faster than exact computation and more accurate than existing approximation methods. We provide volume approximations for the Birkhoff polytopes B 11 ,. .. , B 15 , whereas exact methods have only computed that of B 10 .
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Dates and versions

hal-01897272 , version 1 (28-10-2018)

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Ioannis Z. Emiris, Vissarion Fisikopoulos. Efficient Random-Walk Methods for Approximating Polytope Volume. ACM Transactions on Mathematical Software, 2018, 44 (4), pp.1 - 21. ⟨10.1145/3194656⟩. ⟨hal-01897272⟩
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