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Computing the Antiperiod(s) of a String

Authors Hayam Alamro, Golnaz Badkobeh, Djamal Belazzougui, Costas S. Iliopoulos, Simon J. Puglisi

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Author Details

Hayam Alamro
  • Department of Informatics, King’s College London, UK
  • Department of Information Systems, Princess Nourah bint Abulrahman University, Riyadh, KSA
Golnaz Badkobeh
  • Department of Computing, Goldsmiths, University of London, UK
Djamal Belazzougui
  • Centre de Recherche sur I'nformation Scientifique et Technique, Algeria
Costas S. Iliopoulos
  • Department of Informatics, King’s College London, UK
Simon J. Puglisi
  • Department of Computer Science, University of Helsinki, Finland

Acknowledgements

This work was supported by the Academy of Finland under grant 319454. We thank the anonymous reviewers for their detailed comments that greatly improved the quality of this article, in particular for the improvement in Section 5.2 and for pointers on previous works on weighted-level ancestors data structures.

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Hayam Alamro, Golnaz Badkobeh, Djamal Belazzougui, Costas S. Iliopoulos, and Simon J. Puglisi. Computing the Antiperiod(s) of a String. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, pp. 32:1-32:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.CPM.2019.32

Abstract

A string S[1,n] is a power (or repetition or tandem repeat) of order k and period n/k, if it can be decomposed into k consecutive identical blocks of length n/k. Powers and periods are fundamental structures in the study of strings and algorithms to compute them efficiently have been widely studied. Recently, Fici et al. (Proc. ICALP 2016) introduced an antipower of order k to be a string composed of k distinct blocks of the same length, n/k, called the antiperiod. An arbitrary string will have antiperiod t if it is prefix of an antipower with antiperiod t. In this paper, we describe efficient algorithm for computing the smallest antiperiod of a string S of length n in O(n) time. We also describe an algorithm to compute all the antiperiods of S that runs in O(n log n) time.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial algorithms
Keywords
  • antiperiod
  • antipower
  • power
  • period
  • repetition
  • run
  • string

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