Closest periodic vectors in L p spaces

Amihood Amir, Estrella Eisenberg, Avivit Levy, Noa Lewenstein

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations


The problem of finding the period of a vector V is central to many applications. Let V′ be a periodic vector closest to V under some metric. We seek this V′, or more precisely we seek the smallest period that generates V′. In this paper we consider the problem of finding the closest periodic vector in L p spaces. The measures of "closeness" that we consider are the metrics in the different L p spaces. Specifically, we consider the L 1, L 2 and L metrics. In particular, for a given n-dimensional vector V, we develop O(n 2) time algorithms (a different algorithm for each metric) that construct the smallest period that defines such a periodic n-dimensional vector V′. We call that vector the closest periodic vector of V under the appropriate metric. We also show (three) O(n logn) time constant approximation algorithms for the (appropriate) period of the closest periodic vector.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings
Number of pages10
StatePublished - 2011
Event22nd International Symposium on Algorithms and Computation, ISAAC 2011 - Yokohama, Japan
Duration: 5 Dec 20118 Dec 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7074 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference22nd International Symposium on Algorithms and Computation, ISAAC 2011


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