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A sharp upper bound for the Lattice Programming Gap

Aliev, Iskander 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. 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: 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: 13 Mar 2020 15:48

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