Journal Article

Near-optimal deterministic algorithms for volume computation via M-ellipsoids

Proceedings of the National Academy of Sciences of the United States of America (2013) 110(48) 19237-19245
DOI: 10.1073/pnas.1203863110
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Abstract

We give a deterministic 2O(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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Dadush, D., & Vempala, S. S. (2013). Near-optimal deterministic algorithms for volume computation via M-ellipsoids. Proceedings of the National Academy of Sciences of the United States of America, 110(48), 19237–19245. https://doi.org/10.1073/pnas.1203863110

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