On the complexity of determining the period of a string

Artur Czumaj, Leszek Gaşieniec

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

Abstract

We study the complexity of a classical combinatorial problem of computing the period of a string.We investigate both the average- and the worst-case complexity of the problem. We deliver almost tight bounds for the average-case. We show that every algorithm computing the period must examine (formula presented) symbols of an input string of lengthm. On the other hand we present an algorithm that computes the period by examining on average (formula presented) symbols, where |Σ| ³ 2 stands for the input alphabet. We also present a deterministic algorithm that computes the period of a string usingm+O(m3/4) comparisons. This is the first algorithm that have the worstcase complexity m + o(m)

Original languageEnglish (US)
Title of host publicationCombinatorial Pattern Matching - 11th Annual Symposium, CPM 2000, Proceedings
EditorsRaffaele Giancarlo, David Sankoff
PublisherSpringer Verlag
Pages412-422
Number of pages11
ISBN (Electronic)3540676333, 9783540676331
DOIs
StatePublished - Jan 1 2000
Externally publishedYes
Event11th Annual Symposium on Combinatorial Pattern Matching, CPM 2000 - Montreal, Canada
Duration: Jun 21 2000Jun 23 2000

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1848
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference11th Annual Symposium on Combinatorial Pattern Matching, CPM 2000
CountryCanada
CityMontreal
Period6/21/006/23/00

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Czumaj, A., & Gaşieniec, L. (2000). On the complexity of determining the period of a string. In R. Giancarlo, & D. Sankoff (Eds.), Combinatorial Pattern Matching - 11th Annual Symposium, CPM 2000, Proceedings (pp. 412-422). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1848). Springer Verlag. https://doi.org/10.1007/3-540-45123-4_34