# Multiple serial episode matching

Abstract : In a previous paper we generalized the Knuth-Morris-Pratt (KMP) pattern matching algorithm and defined a non-conventional kind of RAM, the MP--RAMs (RAMS equipped with extra operations), and designed an $O(n)$ on-line algorithm for solving the serial episode matching problem on MP--RAMs when there is only one single episode. We here give two extensions of this algorithm to the case when we search for several patterns simultaneously and compare them. More preciseley, given $q+1$ strings (a text $t$ of length $n$ and $q$ patterns $m_1,\ldots,m_q$) and a natural number $w$, the {\em multiple serial episode matching problem} consists in finding the number of size $w$ windows of text $t$ which contain patterns $m_1,\ldots,m_q$ as subsequences, i.e. for each $m_i$, if $m_i=p_1,\ldots ,p_k$, the letters $p_1,\ldots ,p_k$ occur in the window, in the same order as in $m_i$, but not necessarily consecutively (they may be interleaved with other letters).} The main contribution is an algorithm solving this problem on-line in time $O(nq)$.
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Conference papers

https://hal.archives-ouvertes.fr/hal-00020564
Contributor : Irene Guessarian Connect in order to contact the contributor
Submitted on : Monday, March 13, 2006 - 12:00:15 PM
Last modification on : Friday, November 19, 2021 - 6:06:02 PM
Long-term archiving on: : Saturday, April 3, 2010 - 10:47:52 PM

### Citation

Patrick Cegielski, Irene Guessarian, Yuri Matiyasevich. Multiple serial episode matching. 2005, pp.26-38. ⟨hal-00020564⟩

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