Covering convex bodies and the closest vector problem

Naszódi, Márton and Venzin, Moritz (2022) Covering convex bodies and the closest vector problem. DISCRETE AND COMPUTATIONAL GEOMETRY, 67 (4). pp. 1191-1210. ISSN 0179-5376

Preview

Text s00454-022-00392-x.pdf - Published Version Available under License Creative Commons Attribution. Download (411kB) | Preview

Abstract

We are concerned with the computational problem of determining the covering radius of a rational polytope. This parameter is defined as the minimal dilation factor that is needed for the lattice translates of the correspondingly dilated polytope to cover the whole space. As our main result, we describe a new algorithm for this problem, which is simpler, more efficient and easier to implement than the only prior algorithm of Kannan (1992). Motivated by a variant of the famous Lonely Runner Conjecture, we use its geometric interpretation in terms of covering radii of zonotopes, and apply our algorithm to prove the first open case of three runners with individual starting points.

Actions (login required)

Edit Item