Greedoids and Violator Spaces

The primary objective of this paper is to establish connections between two well-known but previously independently developed theories: the theory of violator spaces and the theory of greedoids. Violator spaces were introduced by Matoušek et al. in 2008 as a generalization of linear programming problems. Greedoids were introduced by Korte and Lovász in 1981 in an effort to characterize combinatorial structures where greedy algorithms yield optimal solutions. In this work, we explore the relationships between violator spaces and greedoids, demonstrating that greedoids can be defined using a variant of a violator operator. These interrelations provide a new characterization of antimatroids.