A linear time algorithm for seeds computation

Authors:
Tomasz Kociumaka;Marcin Kubica;Jakub Radoszewski;Wojciech Rytter;Tomasz Waleń
Affiliations:
University of Warsaw, Warsaw, Poland;University of Warsaw, Warsaw, Poland;University of Warsaw, Warsaw, Poland;University of Warsaw, Warsaw, Poland, and Nicolaus Copernicus University, Toruń, Poland;University of Warsaw, Warsaw, Poland, and International Institute of Molecular and Cell Biology in Warsaw, Poland
Venue:
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Year:
2012

Citing 20
Cited 2

Fast algorithms for finding nearest common ancestors

SIAM Journal on Computing
Transducers and repetitions

Theoretical Computer Science
Detecting leftmost maximal periodicities

Discrete Applied Mathematics - Combinatorics and complexity
Optimal superprimitivity testing for strings

Information Processing Letters
An on-line string superprimitivity test

Information Processing Letters
Efficient detection of quasiperiodicities in strings

Theoretical Computer Science
The subtree max gap problem with application to parallel string covering

Information and Computation
Computing the covers of a string in linear time

SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Quasiperiodicity: From detection to normal forms

Automatica (Journal of IFAC)
Repetitive perhaps, but certainly not boring

Theoretical Computer Science
Finding Maximal Quasiperiodicities in Strings

COM '00 Proceedings of the 11th Annual Symposium on Combinatorial Pattern Matching
Optimal suffix tree construction with large alphabets

FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Finding Maximal Repetitions in a Word in Linear Time

FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
A linear-time algorithm for a special case of disjoint set union

STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Algorithms on Strings

Algorithms on Strings
Computing the λ-covers of a string

Information Sciences: an International Journal
Computing Longest Previous non-overlapping Factors

Information Processing Letters
New complexity results for the k-covers problem

Information Sciences: an International Journal
Efficient seeds computation revisited

CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
Computing the λ-seeds of a string

AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management

Computing regularities in strings: A survey

European Journal of Combinatorics
On left and right seeds of a string

Journal of Discrete Algorithms

Quantified Score

Hi-index	0.01

Visualization

Abstract

A seed in a word is a relaxed version of a period. We show a linear time algorithm computing a compact representation of all the seeds of a word, in particular, the shortest seed. Thus, we solve an open problem stated in the survey by Smyth (2000) and improve upon a previous over 15-year old O(n log n) algorithm by Iliopoulos, Moore and Park (1996). Our approach is based on combinatorial relations between seeds and a variant of the LZ-factorization (used here for the first time in context of seeds).