RAIRO - Theoretical Informatics and Applications

Research Article

Tree inclusion problems

Patrick Cégielskia1, Irène Guessariana2 and Yuri Matiyasevicha3

a1 LACL EA 4213, Université Paris Est, Route forestière Hurtault, 77300 Fontainebleau, France; cegielski@univ-paris12.fr

a2 LIAFA, UMR 7089 and Université Paris 6, 2 place Jussieu, 75254 Paris Cedex 5, France; ig@liafa.jussieu.fr

a3 Steklov Institute of Mathematics, Fontanka 27, St. Petersburg, 191023, Russia; yumat@pdmi.ras.ru

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).

(Online publication January 18 2008)

Key Words:

  • Subtree inclusion;
  • algorithm

Mathematics Subject Classification:

  • 68Q25;
  • 68W05
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