# Tree inclusion problems

Abstract : Given two trees (a target $T$ and a pattern $P$) and a natural number $w$, {\em window embedded subtree problems} consist in deciding whether $P$ occurs as an embedded subtree of $T$ and/or finding the number of size (at most) $w$ windows of $T$ which contain pattern $P$ as an embedded subtree. $P$ is an embedded subtree of $T$ if $P$ can be obtained by deleting some nodes from $T$ (if a node $v$ is deleted, all edges adjacent to $v$ are also deleted, and outgoing edges are replaced by edges going from the parent of $v$ (if it exists) to the children of $v$). Deciding whether $P$ is an embedded subtree of $T$ is known to be NP-complete. Our algorithms run in time $O(|T| 2^{2^{|P|}})$ where $|T|$ (resp. $|P|$) is the size of $T$ (resp. $P$).
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Cited literature [3 references]

https://hal.archives-ouvertes.fr/hal-00159125
Contributor : Irene Guessarian <>
Submitted on : Tuesday, July 3, 2007 - 1:02:30 PM
Last modification on : Saturday, March 28, 2020 - 2:13:30 AM
Document(s) archivé(s) le : Thursday, April 8, 2010 - 7:40:09 PM

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• HAL Id : hal-00159125, version 1

### Citation

Patrick Cegielski, Irene Guessarian, Yuri Matiyasevich. Tree inclusion problems. 2007. ⟨hal-00159125⟩

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