Detecting Approximate Periodic Patterns

Amihood Amir, Alberto Apostolico, Estrella Eisenberg, Gad M. Landau, Avivit Levy, Noa Lewenstein

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


Given ɛ ∈ [0, 1), the ɛ-Relative Error Periodic Pattern Problem (REPP) is the following: INPUT: An n-long sequence S of numbers si ∈ N in increasing order. OUTPUT: The longest ɛ-relative error periodic pattern, i.e., the longest subsequence si1,si2,…,sik of S, for which there exists a number p such that the absolute difference between any two consecutive numbers in the subsequence is at least p and at most p(1 + ɛ). The best known algorithm for this problem has O(n3 ) time complexity. This bound is too high for large inputs in practice. In this paper we give a new algorithm for finding the longest ɛ-relative error periodic pattern (the REPP problem). Our method is based on a transformation of the input sequence into a different representation: the ɛ-active maximal intervals list L, defined in this paper. We show that the transformation of S to the list L can be done efficiently (quadratic in n and linear in the size of L) and prove that our algorithm is linear in the size of L. This enables us to prove that our algorithm works in sub-cubic time on inputs for which the best known algorithm works in O(n3 ) time. Moreover, though it may happen that our algorithm would still be cubic, it is never worse than the known O(n3 )-algorithm and in many situations its complexity is O(n2 )time.

Original languageEnglish
Title of host publicationDesign and Analysis of Algorithms - 1st Mediterranean Conference on Algorithms, MedAlg 2012, Proceedings
EditorsGuy Even, Dror Rawitz
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages12
ISBN (Print)9783642348617
StatePublished - 2012
Event1st Mediterranean Conference on Algorithms, MedAlg 2012 - Kibbutz Ein Gedi, Israel
Duration: 3 Dec 20125 Dec 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7659 LNNS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference1st Mediterranean Conference on Algorithms, MedAlg 2012
CityKibbutz Ein Gedi

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2012.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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