Resistant Sets in the Unit Hypercube

Abstract

Ideal matrices and clutters are prevalent in combinatorial optimization, ranging from balanced matrices, clutters of T-joins, to clutters of rooted arborescences. Most of the known examples of ideal clutters are combinatorial in nature. In this paper, rendered by the recently developed theory of cuboids, we provide a different class of ideal clutters, one that is geometric in nature. The advantage of this new class of ideal clutters is that it allows for infinitely many ideal minimally nonpacking clutters. We characterize the densest ideal minimally nonpacking clutters of the class. Using the tools developed, we then verify the replication conjecture for the class.