The Aggregation Closure is Polyhedral for Packing and Covering Integer Programs

TL;DR

This paper proves that the aggregation closure for packing and covering integer programs is polyhedral, and extends this result to the k-aggregation closure for all k, advancing the understanding of their geometric structure.

Contribution

It establishes that the aggregation closure and its generalization, the k-aggregation closure, are polyhedral, resolving an open question in the field.

Findings

Aggregation closure is polyhedral.

k-aggregation closure is polyhedral for all k.

Advances understanding of the geometric structure of these closures.

Abstract

Recently, Bodur, Del Pia, Dey, Molinaro and Pokutta introduced the concept of aggregation cuts for packing and covering integer programs. The aggregation closure is the intersection of all aggregation cuts. Bodur et. al. studied the strength of this closure, but left open the question of whether the aggregation closure is polyhedral. In this paper, we answer this question in the positive, i.e. we show that the aggregation closure is polyhedral. Finally, we demonstrate that a generalization, the k-aggregation closure, is also polyhedral for all k.