Article
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Greedoids and Violator Spaces
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Version 1
: Received: 31 July 2024 / Approved: 31 July 2024 / Online: 1 August 2024 (05:30:06 CEST)
How to cite: Kempner, Y.; Levit, V. Greedoids and Violator Spaces. Preprints 2024, 2024072585. https://doi.org/10.20944/preprints202407.2585.v1 Kempner, Y.; Levit, V. Greedoids and Violator Spaces. Preprints 2024, 2024072585. https://doi.org/10.20944/preprints202407.2585.v1
Abstract
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.
Keywords
violator space; linear programming; closure operator; greedoid; antimatroid
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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