Multiple serial episodes matching

Authors:
Patrick Cégielski;Irène Guessarian;Yuri Matiyasevich
Affiliations:
LACL, UMR-FRE 2673, Université Paris 12, Route forestière Hurtault, F-77300 Fontainebleau, France;LIAFA, UMR 7089 and Université Paris 6, 2, Place Jussieu, 75254 Paris Cedex 5, France;Steklov Institute of Mathematics, Fontanka 27, St. Petersburg, Russia
Venue:
Information Processing Letters
Year:
2006

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Abstract

Given q+1 strings (a text t of length n and q patterns m"1,...,m"q) and a natural number w, the multiple serial episode matching problem consists in finding the number of size w windows of text t which contain patterns m"1,...,m"q as subsequences, i.e., for each m"i, if m"i=p"1,...,p"k, the letters p"1,...,p"k occur in the window, in the same order as in m"i, but not necessarily consecutively (they may be interleaved with other letters). Our main contribution here is an algorithm solving this problem on-line in time O(nq) with an MP-RAM model (which is a RAM model equipped with extra operations).