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Minimal Absent Words in a Sliding Window and Applications to On-Line Pattern Matching

Research output: Chapter in Book/Report/Conference proceedingOther chapter contribution

Maxime Crochemore, Alice Heliou, Gregory Kucherov, Laurent Mouchard, Solon P. Pissis, Yann Ramusat

Original languageEnglish
Title of host publicationFundamentals of Computation Theory: 21st International Symposium, FCT 2017, Bordeaux, France, September 11--13, 2017, Proceedings
EditorsRalf Klasing, Marc Zeitoun
Place of PublicationBerlin, Heidelberg
PublisherSpringer Berlin Heidelberg
Pages164-176
Number of pages13
Volume10472
ISBN (Print)978-3-662-55751-8
DOIs
Publication statusE-pub ahead of print - 16 Aug 2017

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Berlin Heidelberg

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King's Authors

Abstract

An absent (or forbidden) word of a word y is a word that does not occur in y. It is then called minimal if all its proper factors occur in y. There exist linear-time and linear-space algorithms for computing all minimal absent words of y (Crochemore et al. in Inf Process Lett 67:111–117, 1998; Belazzougui et al. in ESA 8125:133–144, 2013; Barton et al. in BMC Bioinform 15:388, 2014). Minimal absent words are used for data compression (Crochemore et al. in Proc IEEE 88:1756–1768, 2000, Ota and Morita in Theoret Comput Sci 526:108–119, 2014) and for alignment-free sequence comparison by utilizing a metric based on minimal absent words (Chairungsee and Crochemore in Theoret Comput Sci 450:109–116, 2012). They are also used in molecular biology; for instance, three minimal absent words of the human genome were found to play a functional role in a coding region in Ebola virus genomes (Silva et al. in Bioinformatics 31:2421–2425, 2015). In this article we introduce a new application of minimal absent words for on-line pattern matching. Specifically, we present an algorithm that, given a pattern x and a text y, computes the distance between x and every window of size |x| on y. The running time is O(σ|y|)O(σ|y|) , where σσ is the size of the alphabet. Along the way, we show an O(σ|y|)O(σ|y|) -time and O(σ|x|)O(σ|x|) -space algorithm to compute the minimal absent words of every window of size |x| on y, together with some new combinatorial insight on minimal absent words.

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