Near-Optimal Deterministic Algorithms for Volume Computation and Lattice Problems via M-Ellipsoids
Daniel Dadush, Santosh Vempala
TL;DR
This paper presents a deterministic algorithm for computing M-ellipsoids of convex bodies, leading to improved deterministic methods for volume estimation and lattice problems, matching known lower bounds.
Contribution
It introduces a near-optimal deterministic algorithm for M-ellipsoid computation, enhancing volume and lattice problem algorithms under general norms.
Findings
Deterministic 2^{O(n)} algorithm for M-ellipsoid computation
Improved deterministic algorithms for volume estimation
Enhanced algorithms for lattice vector problems
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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