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Tree inclusions in windows and slices

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A labelled tree P is an embedded subtree of a labelled tree 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 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. Given two trees (a target T and a pattern P) and a natural number w, we address two problems: 1) counting the number of windows of T having height exactly w and containing the pattern P as an embedded subtree, and 2) counting the number of slices of T having height exactly w and containing the pattern P as an embedded subtree. Our algorithms run in time O(|T|(w − h(P)+2)4|P|), where |T| (respectively, |P|) is the size of T (respectively, P), and h(P) is the height of P. Bibliography: 10 titles.

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Author information

Authors and Affiliations

  1. LIAFA, UMR 7089 and Université Paris-Diderot, Paris 7, France

    I. Guessarian

  2. LACL, Université Paris Est, IUT, Fontainebleau, France

    P. Cégielski

Authors
  1. I. Guessarian
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  2. P. Cégielski
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Correspondence to I. Guessarian.

Additional information

Dedicated to Yu. Matiyasevich on the occasion of his 60th birthday.

Published in Zapiski Nauchnykh Seminarov POMI, Vol. 358, 2008, pp. 3–53.

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Guessarian, I., Cégielski, P. Tree inclusions in windows and slices. J Math Sci 158, 623–632 (2009). https://doi.org/10.1007/s10958-009-9401-7

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  • DOI: https://doi.org/10.1007/s10958-009-9401-7

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