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The Tree Inclusion Problem: In Optimal Space and Faster

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Automata, Languages and Programming (ICALP 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3580))

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Abstract

Given two rooted, ordered, and labeled trees P and T the tree inclusion problem is to determine if P can be obtained from T by deleting nodes in T. This problem has recently been recognized as an important query primitive in XML databases. Kilpeläinen and Mannila (SIAM J. of Comp. 1995) presented the first polynomial time algorithm using quadratic time and space. Since then several improved results have been obtained for special cases when P and T have a small number of leaves or small depth. However, in the worst case these algorithms still use quadratic time and space. In this paper we present a new approach to the problem which leads to a new algorithm which uses optimal linear space and has subquadratic running time. Our algorithm improves all previous time and space bounds. Most importantly, the space is improved by a linear factor. This will make it possible to query larger XML databases and speed up the query time since more of the computation can be kept in main memory.

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Author information

Authors and Affiliations

  1. Department of Theoretical Computer Science, The IT University of Copenhagen, Rued Langgaards Vej 7, 2300, Copenhagen S, Denmark

    Philip Bille & Inge Li Gørtz

Authors
  1. Philip Bille
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  2. Inge Li Gørtz
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Editor information

Editors and Affiliations

  1. CITI / Departamento de Informática, Universidade Nova de Lisboa, Portugal

    Luís Caires

  2. Dipartimento di Informatica, Sistemi e Produzione, Università di Roma “Tor Vergata”, via del Politecnico 1, 00133, Roma, Italy

    Giuseppe F. Italiano

  3. Departamento de Informatica, Universidade Nova de Lisboa, 2829-516, Caparica, Portugal

    Luís Monteiro

  4. Ecole Polytechnique, Rue de Saclay, 91128, Palaiseau Cedex, France

    Catuscia Palamidessi

  5. Computer Science Department, Google Inc. and Columbia University, 1214 Amsterdam Avenue, NY 10027, New York, USA

    Moti Yung

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© 2005 Springer-Verlag Berlin Heidelberg

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Bille, P., Li Gørtz, I. (2005). The Tree Inclusion Problem: In Optimal Space and Faster. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds) Automata, Languages and Programming. ICALP 2005. Lecture Notes in Computer Science, vol 3580. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11523468_6

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  • DOI: https://doi.org/10.1007/11523468_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-27580-0

  • Online ISBN: 978-3-540-31691-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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