On the right-seed array of a string

Michalis Christou*, Maxime Crochemore, Ondrej Guth, Costas S. Iliopoulos, Solon P. Pissis

*Corresponding author for this work

Research output: Chapter in Book / Report / Conference proceedingConference contributionAcademicpeer-review

Abstract

We consider the problem of finding the repetitive structure of a given fixed string y. A factor u of y is a cover of y, if every letter of y falls within some occurrence of u in y. A factor v of y is a seed of y, if it is a cover of a superstring of y. There exist linear-time algorithms for solving the minimal cover problem. The minimal seed problem is of much higher algorithmic difficulty, and no linear-time algorithm is known. In this article, we solve one of its variants - computing the minimal and maximal right-seed array of a given string. A right seed of y is the shortest suffix of y that it is a cover of a superstring of y. An integer array RS is the minimal right-seed (resp. maximal right-seed) array of y, if RS[i] is the minimal (resp. maximal) length of right seeds of y[0..i]. We present an O(n log n) time algorithm that computes the minimal right-seed array of a given string, and a linear-time solution to compute the maximal right-seed array by detecting border-free prefixes of the given string.

Original languageEnglish
Title of host publicationComputing and Combinatorics - 17th Annual International Conference, COCOON 2011, Proceedings
Pages492-502
Number of pages11
DOIs
Publication statusPublished - 29 Aug 2011
Externally publishedYes
Event17th Annual International Computing and Combinatorics Conference, COCOON 2011 - Dallas, TX, United States
Duration: 14 Aug 201116 Aug 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6842 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference17th Annual International Computing and Combinatorics Conference, COCOON 2011
CountryUnited States
CityDallas, TX
Period14/08/1116/08/11

Keywords

  • algorithms on strings
  • covers
  • periodicity
  • seeds

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