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Tree inclusion problems

Published online by Cambridge University Press:  18 January 2008

Patrick Cégielski ,
Irène Guessarian  and
Yuri Matiyasevich
Patrick Cégielski
Affiliation:
LACL EA 4213, Université Paris Est, Route forestière Hurtault, 77300 Fontainebleau, France; [email protected]
Irène Guessarian
Affiliation:
LIAFA, UMR 7089 and Université Paris 6, 2 place Jussieu, 75254 Paris Cedex 5, France; [email protected]
Yuri Matiyasevich
Affiliation:
Steklov Institute of Mathematics, Fontanka 27, St. Petersburg, 191023, Russia; [email protected]
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Abstract

Given two trees (a target T and a pattern P) and a natural number w, 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|22|P|) where |T| (resp. |P|) is the size of T (resp. P).

Keywords

Subtree inclusionalgorithm
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 42 , Issue 1: A nonstandard spirit among computer scientists:a tribute to Serge Grigorieff at the occasion of his 60th birthday , January 2008 , pp. 5 - 20
Copyright
© EDP Sciences, 2007

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References

Boasson, L., Cegielski, P., Guessarian, I. and Matiyasevich, Yu., Window accumulated subsequence matching is linear. Ann. Pure Appl. Logic 113 (2001) 59–80. CrossRef
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