Integer packing sets form a well-quasi-ordering

Alberto Del Pia; Dion Gijswijt; Jeff Linderoth; Haoran Zhu

doi:10.1016/j.orl.2021.01.013

Integer packing sets form a well-quasi-ordering

Alberto Del Pia, Dion Gijswijt, Jeff Linderoth, Haoran Zhu^*

^*Corresponding author for this work

Discrete Mathematics and Optimization

Research output: Contribution to journal › Article › Scientific › peer-review

2 Citations (Scopus)

85 Downloads (Pure)

Abstract

An integer packing set is a set of non-negative integer vectors with the property that, if a vector x is in the set, then every non-negative integer vector y with y≤x is in the set as well. The main result of this paper is that integer packing sets, ordered by inclusion, form a well-quasi-ordering. This result allows us to answer a recently posed question: the k-aggregation closure of any packing polyhedron is again a packing polyhedron.

Original language	English
Pages (from-to)	226-230
Number of pages	5
Journal	Operations Research Letters
Volume	49
Issue number	2
DOIs	https://doi.org/10.1016/j.orl.2021.01.013
Publication status	Published - 2021

Bibliographical note

Accepted Author Manuscript

Keywords

k-aggregation closure
Packing polyhedra
Polyhedrality
Well-quasi-ordering

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10.1016/j.orl.2021.01.013

IPS_WQOAccepted author manuscript, 257 KBLicence: CC BY-NC-ND

Cite this

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title = "Integer packing sets form a well-quasi-ordering",

abstract = "An integer packing set is a set of non-negative integer vectors with the property that, if a vector x is in the set, then every non-negative integer vector y with y≤x is in the set as well. The main result of this paper is that integer packing sets, ordered by inclusion, form a well-quasi-ordering. This result allows us to answer a recently posed question: the k-aggregation closure of any packing polyhedron is again a packing polyhedron.",

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T1 - Integer packing sets form a well-quasi-ordering

AU - Del Pia, Alberto

AU - Gijswijt, Dion

AU - Linderoth, Jeff

AU - Zhu, Haoran

N1 - Accepted Author Manuscript

PY - 2021

Y1 - 2021

N2 - An integer packing set is a set of non-negative integer vectors with the property that, if a vector x is in the set, then every non-negative integer vector y with y≤x is in the set as well. The main result of this paper is that integer packing sets, ordered by inclusion, form a well-quasi-ordering. This result allows us to answer a recently posed question: the k-aggregation closure of any packing polyhedron is again a packing polyhedron.

AB - An integer packing set is a set of non-negative integer vectors with the property that, if a vector x is in the set, then every non-negative integer vector y with y≤x is in the set as well. The main result of this paper is that integer packing sets, ordered by inclusion, form a well-quasi-ordering. This result allows us to answer a recently posed question: the k-aggregation closure of any packing polyhedron is again a packing polyhedron.

KW - k-aggregation closure

KW - Packing polyhedra

KW - Polyhedrality

KW - Well-quasi-ordering

UR - https://www.scopus.com/pages/publications/85099886472

U2 - 10.1016/j.orl.2021.01.013

DO - 10.1016/j.orl.2021.01.013

M3 - Article

AN - SCOPUS:85099886472

SN - 0167-6377

VL - 49

SP - 226

EP - 230

JO - Operations Research Letters

JF - Operations Research Letters

IS - 2

ER -

Integer packing sets form a well-quasi-ordering

Abstract

Bibliographical note

Keywords

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