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• W2949397144 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." @default.
• W2949397144 created "2019-06-27" @default.
• W2949397144 creator A5080051337 @default.
• W2949397144 creator A5087662998 @default.
• W2949397144 date "2013-12-10" @default.
• W2949397144 modified "2023-09-27" @default.
• W2949397144 title "Efficient Random-Walk Methods for Approximating Polytope Volume" @default.
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• W2949397144 hasPublicationYear "2013" @default.
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