Algorithms for anti-powers in strings

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Badkobeh , G , Fici , G & Puglisi , S J 2018 , ' Algorithms for anti-powers in strings ' , Information Processing Letters , vol. 137 , pp. 57-60 .

Title: Algorithms for anti-powers in strings
Author: Badkobeh, Golnaz; Fici, Gabriele; Puglisi, Simon J.
Contributor organization: Department of Computer Science
Helsinki Institute for Information Technology
Algorithmic Bioinformatics
Date: 2018-09
Language: eng
Number of pages: 4
Belongs to series: Information Processing Letters
ISSN: 0020-0190
Abstract: A string S[1,n] is a power (or tandem repeat) of order k and period n/k if it can be decomposed into k consecutive equal-length blocks of letters. Powers and periods are fundamental to string processing, and algorithms for their efficient computation have wide application and are heavily studied. Recently, Fici et al. (Proc. ICALP 2016) defined an anti-power of order k to be a string composed of k pairwise-distinct blocks of the same length (n/k, called anti-period). Anti-powers are a natural converse to powers, and are objects of combinatorial interest in their own right. In this paper we initiate the algorithmic study of anti-powers. Given a string S, we describe an optimal algorithm for locating all substrings of S that are anti-powers of a specified order. The optimality of the algorithm follows form a combinatorial lemma that provides a lower bound on the number of distinct anti-powers of a given order: we prove that a string of length n can contain Θ(n2/k) distinct anti-powers of order k.
Subject: Anti-powers
Combinatorics on words
113 Computer and information sciences
Peer reviewed: Yes
Rights: cc_by_nc_nd
Usage restriction: openAccess
Self-archived version: acceptedVersion

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