{"title":"Approximating the densest sublattice from Rankin’s inequality","authors":"Jianwei Li, Phong Q. Nguyen","doi":"10.1112/S1461157014000333","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":54381,"journal":{"name":"Lms Journal of Computation and Mathematics","volume":"17 1","pages":"92-111"},"PeriodicalIF":0.0000,"publicationDate":"2014-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1112/S1461157014000333","citationCount":"14","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lms Journal of Computation and Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1112/S1461157014000333","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 14
Abstract
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.
期刊介绍：
LMS Journal of Computation and Mathematics has ceased publication. Its final volume is Volume 20 (2017). LMS Journal of Computation and Mathematics is an electronic-only resource that comprises papers on the computational aspects of mathematics, mathematical aspects of computation, and papers in mathematics which benefit from having been published electronically. The journal is refereed to the same high standard as the established LMS journals, and carries a commitment from the LMS to keep it archived into the indefinite future. Access is free until further notice.
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