Near-Optimal Deterministic Algorithms For Volume Computation Via M-Ellipsoids

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA（2013）

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摘要

We give a deterministic 2(o(n)) algorithm for computing an M-ellipsoid of a convex body, matching a known lower bound. This leads to a nearly optimal deterministic algorithm for estimating the volume of a convex body and improved deterministic algorithms for fundamental lattice problems under general norms.

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关键词

shortest lattice vector, convex program, covering numbers

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