A Parametric Version of LLL and Some Consequences: Parametric Shortest and Closest Vector Problems

DOI10.1137/20M1327422zbMath1464.11065arXiv1909.04762OpenAlexW3102077787MaRDI QIDQ5139657

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Publication date: 10 December 2020

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.04762

zbMATH Keywords

shortest vector problemLLL algorithmclosest vector problemquasi-polynomialsparametric lattices

Mathematics Subject Classification ID

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Lattices and convex bodies (number-theoretic aspects) (11H06)

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Cites Work

• Note on shortest and nearest lattice vectors
• The unreasonable ubiquitousness of quasi-polynomials
• Integer points in polyhedra
• On Lovász' lattice reduction and the nearest lattice point problem
• Factoring polynomials with rational coefficients
• The Shortest Vector in a Lattice is Hard to Approximate to within Some Constant
• Integer hulls of linear polyhedra and scl in families
• Mathematics of Public Key Cryptography
• Parametrizing an Integer Linear Program by an Integer
• Parametric Presburger arithmetic: logic, combinatorics, and quasi-polynomial behavior
• Generalized Ehrhart polynomials
• Unnamed Item
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