Near-Optimal Deterministic Algorithms for Volume Computation and Lattice Problems via M-Ellipsoids

Daniel Dadush; Santosh Vempala

doi:10.1073/pnas.1203863110

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arXiv · 1201.5972

Near-Optimal Deterministic Algorithms for Volume Computation and Lattice Problems via M-Ellipsoids

Daniel Dadush·Santosh Vempala

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Abstract

We give a deterministic 2^{O(n)} algorithm for computing an M-ellipsoid of a convex body, matching a known lower bound. This has several interesting consequences including improved deterministic algorithms for volume estimation of convex bodies and the shortest and closest lattice vector problems under general norms.

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Daniel Dadush, Santosh Vempala. 2012-01-28. Near-Optimal Deterministic Algorithms for Volume Computation and Lattice Problems via M-Ellipsoids. https://doi.org/10.1073/pnas.1203863110

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