Algorithms for anti-powers in strings

Gabriele Fici, Golnaz Badkobeh, Simon J. Puglisi

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)57-60
Number of pages4
JournalInformation Processing Letters
Volume137
Publication statusPublished - 2018

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications

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