Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-27T07:34:44.512Z Has data issue: false hasContentIssue false
  • English
  • Français

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; cegielski@univ-paris12.fr
Irène Guessarian
Affiliation:
LIAFA, UMR 7089 and Université Paris 6, 2 place Jussieu, 75254 Paris Cedex 5, France; ig@liafa.jussieu.fr
Yuri Matiyasevich
Affiliation:
Steklov Institute of Mathematics, Fontanka 27, St. Petersburg, 191023, Russia; yumat@pdmi.ras.ru
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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
Chi, Y., Muntz, R., Nijssen, S. and Kok, J., Frequent subtree mining – an overview. Fund. Inform. 66 (2005) 161–198.
P. Kilpelainen, Tree matching problems with applications to structured text databases. Ph.D. thesis, Helsinki (1992). http://ethesis.helsinki.fi/julkaisut/mat/tieto/vk/kilpelainen/
Kilpelainen, P. and Mannila, H., Ordered and unordered tree inclusion. SIAM J. Comput. 24 (1995) 340–356. CrossRef