Near-Optimal Computation of Runs over General Alphabet via Non-Crossing LCE Queries

Maxime Crochemore, Costas S. Iliopoulos, Tomasz Kociumaka, Ritu Kundu, Solon P. Pissis, Jakub Radoszewski, Wojciech Rytter, Tomasz Walen

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

14 Citations (Scopus)
143 Downloads (Pure)


Longest common extension queries (LCE queries) and runs are ubiquitous in algorithmic stringology. Linear-time algorithms computing runs and preprocessing for constant-time LCE queries have been known for over a decade. However, these algorithms assume a linearly-sortable integer alphabet. A recent breakthrough paper by Bannai et al. (SODA 2015) showed a link between the two notions: all the runs in a string can be computed via a linear number of LCE queries. The first to consider these problems over a general ordered alphabet was Kosolobov (Inf. Process. Lett., 2016), who presented an O(n(logn)2/3)-time algorithm for answering O(n) LCE queries. This result was improved by Gawrychowski et al. (CPM 2016) to O(nloglogn) time. In this work we note a special non-crossing property of LCE queries asked in the runs computation. We show that any n such non-crossing queries can be answered on-line in O(nα(n)) time, where α(n) is the inverse Ackermann function, which yields an O(nα(n))-time algorithm for computing runs.
Original languageEnglish
Title of host publicationString Processing and Information Retrieval
Subtitle of host publication23rd International Symposium, SPIRE 2016, Beppu, Japan, October 18-20, 2016, Proceedings
EditorsShunsuke Inenaga, Kunihiko Sadakane, Tetsuya Sakai
Place of PublicationCham
PublisherSpringer International Publishing Switzerland
Number of pages13
ISBN (Print)9783319460499
Publication statusE-pub ahead of print - 21 Sept 2016

Publication series

NameLecture Notes in Computer Science
ISSN (Print)0302-9743


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