Knapsack polytopes: a survey

Christopher Hojny, Tristan Gally, Oliver Habeck, Hendrik Lüthen, Frederic Matter, Marc E. Pfetsch () and Andreas Schmitt
Additional contact information
Christopher Hojny: Technische Universität Darmstadt
Tristan Gally: Technische Universität Darmstadt
Oliver Habeck: Technische Universität Darmstadt
Hendrik Lüthen: Technische Universität Darmstadt
Frederic Matter: Technische Universität Darmstadt
Marc E. Pfetsch: Technische Universität Darmstadt
Andreas Schmitt: Technische Universität Darmstadt

Annals of Operations Research, 2020, vol. 292, issue 1, No 19, 469-517

Abstract: Abstract The 0/1 knapsack polytope is the convex hull of all 0/1 vectors that satisfy a given single linear inequality with non-negative coefficients. This paper provides a comprehensive overview of knapsack polytopes. We discuss basic polyhedral properties, (lifted) cover and other valid inequalities, cases for which complete linear descriptions are known, geometric properties for small dimensions, and connections to independence systems. We also discuss the generalization to (mixed-)integer knapsack polytopes and variants.

Keywords: Knapsack polytope; Cover inequality; Lifting; Separation problem; Complete linear description; Independence systems (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10479-019-03380-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:292:y:2020:i:1:d:10.1007_s10479-019-03380-2

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-019-03380-2

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().