Near-Optimal Deterministic Algorithms for Volume Computation and Lattice Problems via M-Ellipsoids
Computational Complexity
2014-03-05 v2 Data Structures and Algorithms
Functional Analysis
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.
Cite
@article{arxiv.1201.5972,
title = {Near-Optimal Deterministic Algorithms for Volume Computation and Lattice Problems via M-Ellipsoids},
author = {Daniel Dadush and Santosh Vempala},
journal= {arXiv preprint arXiv:1201.5972},
year = {2014}
}