TY - GEN
T1 - Closest periodic vectors in L p spaces
AU - Amir, Amihood
AU - Eisenberg, Estrella
AU - Levy, Avivit
AU - Lewenstein, Noa
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84055193614&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-25591-5_73
DO - 10.1007/978-3-642-25591-5_73
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AN - SCOPUS:84055193614
SN - 9783642255908
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 714
EP - 723
BT - Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings
T2 - 22nd International Symposium on Algorithms and Computation, ISAAC 2011
Y2 - 5 December 2011 through 8 December 2011
ER -