Absent words in a sliding window with applications

An absent 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. In fact, minimal absent words (MAWs) provide useful information about y and thus have several applications. In this paper, we propose an algorithm that maintains the set of...

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Bibliographic Details
Published inInformation and computation Vol. 270; p. 104461
Main Authors Crochemore, Maxime, Héliou, Alice, Kucherov, Gregory, Mouchard, Laurent, Pissis, Solon P., Ramusat, Yann
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.02.2020
Elsevier
Subjects
Absent words
Algorithms on strings
Computer Science
Data Structures and Algorithms
Forbidden words
Online algorithms
Pattern matching
Online algorithms
Algorithms on strings
Pattern matching
Forbidden words
Absent words
Online AccessGet full text
ISSN0890-5401
1090-2651
DOI10.1016/j.ic.2019.104461

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Summary:An absent 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. In fact, minimal absent words (MAWs) provide useful information about y and thus have several applications. In this paper, we propose an algorithm that maintains the set of MAWs of a fixed-length window sliding over y online. Our algorithm represents MAWs through nodes of the suffix tree. Specifically, the suffix tree of the sliding window is maintained using modified Senft's algorithm (Senft, 2005), itself generalizing Ukkonen's online algorithm (Ukkonen, 1995). We then apply this algorithm to the approximate pattern-matching problem under the Length Weighted Index distance (Chairungsee and Crochemore, 2012). This results in an online O(σ|y|)-time algorithm for finding approximate occurrences of a word x in y, |x|≤|y|, where σ is the alphabet size.
ISSN:0890-5401
1090-2651
DOI:10.1016/j.ic.2019.104461