Optimality of some algorithms to detect quasiperiodicities

  • Authors:
  • R. Groult;G. Richomme

  • Affiliations:
  • -;-

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2010

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Abstract

Improving a 1993 algorithm of Apostolico and Ehrenfeucht, independently Iliopoulos and Mouchard in 1999 and Brodal and Pedersen in 2000 provided O(nlog(n)) algorithms to determine all maximal quasiperiodicities of a word of length n. We show here the optimality of this bound providing an infinite family of words w containing O(|w|log|w|) maximal quasiperiodicities. We also show that this bound is not reached for the celebrated family of Fibonacci words.