Weighted ancestors in suffix trees

Paweł Gawrychowski, Moshe Lewenstein, Patrick K. Nicholson

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

35 Scopus citations

Abstract

The classical, ubiquitous, predecessor problem is to construct a data structure for a set of integers that supports fast predecessor queries. Its generalisation to weighted trees, a.k.a. the weighted ancestor problem, has been extensively explored and successfully reduced to the predecessor problem. It is known that any data structure solution for the weighted ancestor problem that occupies O(n polylog(n)) space must have Ω(loglogn) query time, if the weights are drawn from a polynomially bounded universe. Perhaps the most important and frequent application of the weighted ancestors problem is for suffix trees. It has been a long-standing open question whether the weighted ancestors problem has better bounds for suffix trees. We answer this question positively: we show that a suffix tree built for a text w[1.n] can be preprocessed using O(n) extra space, so that queries can be answered in O(1) time. Thus we improve the running times of several applications. Our improvement is based on a number of data structure tools and a periodicity-based insight into the combinatorial structure of a suffix tree.

Original languageEnglish
Title of host publicationAlgorithms, ESA 2014 - 22nd Annual European Symposium, Proceedings
PublisherSpringer Verlag
Pages455-466
Number of pages12
ISBN (Print)9783662447765
DOIs
StatePublished - 2014
Event22nd Annual European Symposium on Algorithms, ESA 2014 - Wroclaw, Poland
Duration: 8 Sep 201410 Sep 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8737 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference22nd Annual European Symposium on Algorithms, ESA 2014
Country/TerritoryPoland
CityWroclaw
Period8/09/1410/09/14

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