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• W2041990574 abstract "Given a high dimensional convex body K⊆ℝn by a separation oracle, we can approximate its volume with relative error ε, using O*(n5) oracle calls. Our algorithm also brings the body into isotropic position. As all previous randomized volume algorithms, we use “rounding” followed by a multiphase Monte-Carlo (product estimator) technique. Both parts rely on sampling (generating random points in K), which is done by random walk. Our algorithm introduces three new ideas: the use of the isotropic position (or at least an approximation of it) for rounding; the separation of global obstructions (diameter) and local obstructions (boundary problems) for fast mixing; and a stepwise interlacing of rounding and sampling. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 11, 1–50, 1997" @default.
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• W2041990574 date "1997-08-01" @default.
• W2041990574 modified "2023-10-12" @default.
• W2041990574 title "Random walks and anO*(n5) volume algorithm for convex bodies" @default.
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• W2041990574 doi "https://doi.org/10.1002/(sici)1098-2418(199708)11:1<1::aid-rsa1>3.0.co;2-x" @default.
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