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Approximating the densest sublattice from Rankin’s inequality

Part of: Algorithms - Computer Science Computational number theory Geometry of numbers

Published online by Cambridge University Press:  01 August 2014

Jianwei Li  and
Phong Q. Nguyen
Jianwei Li
Affiliation:
Institute for Advanced Study, Tsinghua University, Beijing 100084, China email lijianwei10@mails.tsinghua.edu.cn
Phong Q. Nguyen
Affiliation:
INRIA, France Institute for Advanced Study, Tsinghua University, Beijing 100084, China, http://www.di.ens.fr/∼pnguyen/

Abstract

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We present a higher-dimensional generalization of the Gama–Nguyen algorithm (STOC ’08) for approximating the shortest vector problem in a lattice. This generalization approximates the densest sublattice by using a subroutine solving the exact problem in low dimension, such as the Dadush–Micciancio algorithm (SODA ’13). Our approximation factor corresponds to a natural inequality on Rankin’s constant derived from Rankin’s inequality.

MSC classification

Secondary: 11H06: Lattices and convex bodies 68W25: Approximation algorithms 11Y16: Algorithms; complexity
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 17 , Special Issue A: Algorithmic Number Theory Symposium XI , 2014 , pp. 92 - 111
Copyright
© The Author(s) 2014 

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