A sharp upper bound for the Lattice Programming Gap

Aliev, Iskander ORCID: https://orcid.org/0000-0002-2206-9207 2016. A sharp upper bound for the Lattice Programming Gap. Moscow Journal of Combinatorics and Number Theory 6 (2-3) , pp. 121-129.

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Abstract

Abstract. Given a full-dimensional lattice Λ ⊂ Z d and a vector l ∈ Qd >0 , we consider the family of the lattice problems Minimize {l · x : x ≡ r( mod Λ), x ∈ Z d ≥0} , r ∈ Z d (0.1) . The lattice programming gap gap(Λ,l) is the largest value of the minima in (0.1) as r varies over Z d . We obtain a sharp upper bound for gap(Λ,l).

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	group relaxations; integer programming gap; lattices; covering radius; Frobenius numbers
Publisher:	Moscow Institute of Physics and Technology
ISSN:	2220-5438
Date of First Compliant Deposit:	25 January 2017
Date of Acceptance:	10 August 2016
Last Modified:	20 Nov 2024 21:15
URI:	https://orca.cardiff.ac.uk/id/eprint/97618

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