eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-06-06
32:1
32:11
10.4230/LIPIcs.CPM.2019.32
article
Computing the Antiperiod(s) of a String
Alamro, Hayam
1
2
Badkobeh, Golnaz
3
Belazzougui, Djamal
4
Iliopoulos, Costas S.
1
Puglisi, Simon J.
5
Department of Informatics, King’s College London, UK
Department of Information Systems, Princess Nourah bint Abulrahman University, Riyadh, KSA
Department of Computing, Goldsmiths, University of London, UK
Centre de Recherche sur I'nformation Scientiﬁque et Technique, Algeria
Department of Computer Science, University of Helsinki, Finland
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol128-cpm2019/LIPIcs.CPM.2019.32/LIPIcs.CPM.2019.32.pdf
antiperiod
antipower
power
period
repetition
run
string