The k-aggregation Closure for Covering Sets

TL;DR

This paper proves that the k-aggregation closure of a covering set is a polyhedron, using convex geometry techniques, addressing a question from prior research and potentially aiding future polyhedrality studies.

Contribution

It establishes the polyhedrality of the k-aggregation closure for covering sets, providing a new proof technique based on convex geometry.

Findings

k-aggregation closure of covering sets is polyhedral

Introduces a convex geometry-based proof technique

Addresses a question from Bodur et al. (2017)

Abstract

In this paper, we will answer one of the questions proposed by Bodur, Del~Pia, Dey, Molinaro and Pokutta in 2017. Specifically, we show that the k-aggregation closure of a covering set is a polyhedron. The proof technique is based on an equivalent condition for the closure of any particular family of cutting-planes to be polyhedral, from the perspective of convex geometry. We believe that this technique can be applied to tackle other polyhedrality problems in the future and may be of independent interest.