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Absent words in a sliding window with applications

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

Original languageEnglish
Article number104461
Early online date4 Sep 2019
Accepted/In press28 Jan 2019
E-pub ahead of print4 Sep 2019
Published1 Feb 2020

King's Authors


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.

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