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- W4247333762 abstract "Previous chapter Next chapter Full AccessProceedings Proceedings of the 2013 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)Algorithms for the Densest Sub-Lattice ProblemDaniel Dadush and Daniele MicciancioDaniel Dadush and Daniele Miccianciopp.1103 - 1122Chapter DOI:https://doi.org/10.1137/1.9781611973105.79PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract We give algorithms for computing the densest k-dimensional sublattice of an arbitrary lattice, and related problems. This is an important problem in the algorithmic geometry of numbers that includes as special cases Rankin's problem (which corresponds to the densest sublattice problem with respect to the Euclidean norm, and has applications to the design of lattice reduction algorithms), and the shortest vector problem for arbitrary norms (which corresponds to setting k = 1) and its dual (k = n − 1). Our algorithm works for any norm and has running time kO(k · n) and uses 2n poly(n) space. In particular, the algorithm runs in single exponential time 2O(n) for any constant k = O(1). Previous chapter Next chapter RelatedDetails Published:2013ISBN:978-1-61197-251-1eISBN:978-1-61197-310-5 https://doi.org/10.1137/1.9781611973105Book Series Name:ProceedingsBook Code:PR143Book Pages:xix + 1915" @default.
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- W4247333762 date "2013-01-06" @default.
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- W4247333762 title "Algorithms for the Densest Sub-Lattice Problem" @default.
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