Linear Computation of the Maximum Simultaneous Forward and Backward Bisimulation for Node-Labeled Trees

  • Nils Grimsmo
  • Truls Amundsen Bjørklund
  • Magnus Lie Hetland
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6309)


The F&B-index is used to speed up pattern matching in tree and graph data, and is based on the maximum F&B-bisimulation, which can be computed in loglinear time for graphs. It has been shown that the maximum F-bisimulation can be computed in linear time for DAGs. We build on this result, and introduce a linear algorithm for computing the maximum F&B-bisimulation for tree data. It first computes the maximum F-bisimulation, and then refines this to a maximal B-bisimulation. We prove that the result equals the maximum F&B-bisimulation.


Linear Computation Twig Pattern Successor Rank Splitter Block Twig Query 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bača, R., Krátký, M., Snášel, V.: On the efficient search of an XML twig query in large DataGuide trees. In: Proc. IDEAS (2008)Google Scholar
  2. 2.
    Chen, Q., Lim, A., Ong, K.W.: D(k)-index: an adaptive structural summary for graph-structured data. In: Proc. SIGMOD (2003)Google Scholar
  3. 3.
    Dovier, A., Piazza, C., Policriti, A.: A fast bisimulation algorithm. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, p. 79. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Fernandez, J.-C.: An implementation of an efficient algorithm for bisimulation equivalence. Sci. Comput. Program. 13(2-3) (1990)Google Scholar
  5. 5.
    Goldman, R., Widom, J.: DataGuides: Enabling query formulation and optimization in semistructured databases. In: Proc. VLDB (1997)Google Scholar
  6. 6.
    Gou, G., Chirkova, R.: Efficiently querying large XML data repositories: A survey. Knowl. and Data Eng. (2007)Google Scholar
  7. 7.
    Grimsmo, N., Bjørklund, T.A., Hetland, M.L.: Linear computation of the maximum simultaneous forward and backward bisimulation for node-labeled trees (extended version). Technical Report IDI-TR-2010-10, NTNU, Trondheim, Norway (2010)Google Scholar
  8. 8.
    Henzinger, M.R., Henzinger, T.A., Kopke, P.W.: Computing simulations on finite and infinite graphs. In: Proc. FOCS (1995)Google Scholar
  9. 9.
    Kaushik, R., Bohannon, P., Naughton, J.F., Korth, H.F.: Covering indexes for branching path queries. In: Proc. SIGMOD (2002)Google Scholar
  10. 10.
    Kaushik, R., Bohannon, P., Naughton, J.F., Shenoy, P.: Updates for structure indexes. In: Proc. VLDB (2002)Google Scholar
  11. 11.
    Kaushik, R., Shenoy, P., Bohannon, P., Gudes, E.: Exploiting local similarity for indexing paths in graph-structured data. In: Proc. ICDE (2002)Google Scholar
  12. 12.
    Liu, X., Li, J., Wang, H.: SAM: An efficient algorithm for F&B-index construction. In: Proc. APWeb/WAIM (2007)Google Scholar
  13. 13.
    Milner, R.: Communication and concurrency. Prentice-Hall, Inc., Englewood Cliffs (1989)zbMATHGoogle Scholar
  14. 14.
    Milo, T., Suciu, D.: Index structures for path expressions. In: Beeri, C., Bruneman, P. (eds.) ICDT 1999. LNCS, vol. 1540, pp. 277–295. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  15. 15.
    Paige, R., Tarjan, R.E.: Three partition refinement algorithms. SIAM J. Comput. (1987)Google Scholar
  16. 16.
    Saha, D.: An incremental bisimulation algorithm. In: Proc. FSTTCS (2007)Google Scholar
  17. 17.
    Wu, X., Liu, G.: XML twig pattern matching using version tree. Data & Knowl. Eng. (2008)Google Scholar
  18. 18.
    Yang, B., Fontoura, M., Shekita, E., Rajagopalan, S., Beyer, K.: Virtual cursors for XML joins. In: Proc. CIKM (2004)Google Scholar
  19. 19.
    Yi, K., He, H., Stanoi, I., Yang, J.: Incremental maintenance of XML structural indexes. In: Proc. SIGMOD (2004)Google Scholar
  20. 20.
    Yu, J.X., Cheng, J.: Graph reachability queries: A survey. In: Managing and Mining Graph Data (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Nils Grimsmo
    • 1
  • Truls Amundsen Bjørklund
    • 1
  • Magnus Lie Hetland
    • 1
  1. 1.Norwegian University of Science and TechnologyNorway

Personalised recommendations