Greedoids and Violator Spaces

This research explores the interplay between violator spaces and greedoids—two distinct theoretical frameworks developed independently. Violator spaces were introduced as a generalization of linear programming, while greedoids were designed to characterize combinatorial structures where greedy algor...

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Bibliographic Details
Published inAxioms Vol. 13; no. 9; p. 633
Main Authors Kempner, Yulia, Levit, Vadim E.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.09.2024
Subjects
Algorithms
antimatroid
closure operator
Combinatorial analysis
Euclidean space
Graph theory
greedoid
Greedy algorithms
Linear programming
Mathematical research
violator space
Israel
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Summary:This research explores the interplay between violator spaces and greedoids—two distinct theoretical frameworks developed independently. Violator spaces were introduced as a generalization of linear programming, while greedoids were designed to characterize combinatorial structures where greedy algorithms yield optimal solutions. These frameworks have, until now, existed in isolation. This paper bridges the gap by showing that greedoids can be defined using a modified violator operator. The established connections not only deepen our understanding of these theories but also provide a new characterization of antimatroids.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms13090633