{"title":"最短向量问题的新型近似算法","authors":"K. B. Ajitha Shenoy","doi":"10.1109/ACCESS.2024.3469368","DOIUrl":null,"url":null,"abstract":"Finding the shortest vector in a lattice is a NP-hard problem. The best known approximation algorithm for this problem is LLL algorithm with the approximation factor of \n<inline-formula> <tex-math>$\\alpha ^{\\frac {n-1}{2}}$ </tex-math></inline-formula>\n, \n<inline-formula> <tex-math>$\\alpha \\geq \\frac {4}{3}$ </tex-math></inline-formula>\n, which is not a good approximation factor. This work proposes a new polynomial time approximation algorithm for the shortest lattice vector problem. The proposed method makes use of only integer arithmetic and does not require Gram-Schmidt orthogonal basis for generating reduced basis. The proposed method is able to obtain an approximation factor of \n<inline-formula> <tex-math>$\\frac {1}{(1-\\delta)}$ </tex-math></inline-formula>\n, where \n<inline-formula> <tex-math>$0 \\leq \\delta \\lt 1$ </tex-math></inline-formula>\n.","PeriodicalId":13079,"journal":{"name":"IEEE Access","volume":null,"pages":null},"PeriodicalIF":3.4000,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10697125","citationCount":"0","resultStr":"{\"title\":\"A Novel Approximation Algorithm for the Shortest Vector Problem\",\"authors\":\"K. B. Ajitha Shenoy\",\"doi\":\"10.1109/ACCESS.2024.3469368\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Finding the shortest vector in a lattice is a NP-hard problem. The best known approximation algorithm for this problem is LLL algorithm with the approximation factor of \\n<inline-formula> <tex-math>$\\\\alpha ^{\\\\frac {n-1}{2}}$ </tex-math></inline-formula>\\n, \\n<inline-formula> <tex-math>$\\\\alpha \\\\geq \\\\frac {4}{3}$ </tex-math></inline-formula>\\n, which is not a good approximation factor. This work proposes a new polynomial time approximation algorithm for the shortest lattice vector problem. The proposed method makes use of only integer arithmetic and does not require Gram-Schmidt orthogonal basis for generating reduced basis. The proposed method is able to obtain an approximation factor of \\n<inline-formula> <tex-math>$\\\\frac {1}{(1-\\\\delta)}$ </tex-math></inline-formula>\\n, where \\n<inline-formula> <tex-math>$0 \\\\leq \\\\delta \\\\lt 1$ </tex-math></inline-formula>\\n.\",\"PeriodicalId\":13079,\"journal\":{\"name\":\"IEEE Access\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.4000,\"publicationDate\":\"2024-09-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10697125\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IEEE Access\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://ieeexplore.ieee.org/document/10697125/\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"COMPUTER SCIENCE, INFORMATION SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Access","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10697125/","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
A Novel Approximation Algorithm for the Shortest Vector Problem
Finding the shortest vector in a lattice is a NP-hard problem. The best known approximation algorithm for this problem is LLL algorithm with the approximation factor of
$\alpha ^{\frac {n-1}{2}}$
,
$\alpha \geq \frac {4}{3}$
, which is not a good approximation factor. This work proposes a new polynomial time approximation algorithm for the shortest lattice vector problem. The proposed method makes use of only integer arithmetic and does not require Gram-Schmidt orthogonal basis for generating reduced basis. The proposed method is able to obtain an approximation factor of
$\frac {1}{(1-\delta)}$
, where
$0 \leq \delta \lt 1$
.
IEEE AccessCOMPUTER SCIENCE, INFORMATION SYSTEMSENGIN-ENGINEERING, ELECTRICAL & ELECTRONIC
CiteScore
9.80
自引率
7.70%
发文量
6673
审稿时长
6 weeks
期刊介绍:
IEEE Access® is a multidisciplinary, open access (OA), applications-oriented, all-electronic archival journal that continuously presents the results of original research or development across all of IEEE''s fields of interest.
IEEE Access will publish articles that are of high interest to readers, original, technically correct, and clearly presented. Supported by author publication charges (APC), its hallmarks are a rapid peer review and publication process with open access to all readers. Unlike IEEE''s traditional Transactions or Journals, reviews are "binary", in that reviewers will either Accept or Reject an article in the form it is submitted in order to achieve rapid turnaround. Especially encouraged are submissions on:
Multidisciplinary topics, or applications-oriented articles and negative results that do not fit within the scope of IEEE''s traditional journals.
Practical articles discussing new experiments or measurement techniques, interesting solutions to engineering.
Development of new or improved fabrication or manufacturing techniques.
Reviews or survey articles of new or evolving fields oriented to assist others in understanding the new area.