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Range Searching over Tree Cross Products

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Algorithms - ESA 2000 (ESA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1879))

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Abstract

We introduce the tree cross-product problem, which abstracts a data structure common to applications in graph visualization, string matching, and software analysis. We design solutions with a variety of tradeoffs, yielding improvements and new results for these applications.

Work supported by NSF Grant CCR-9732300 and ARO Grant DAAH04-96-1-0013.

Work completed while a member of AT&T Labs.

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References

  1. S. Alstrup, D. Harel, P. W. Lauridsen, and M. Thorup. Dominators in linear time. SIAM J. 28(6):2117–32, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  2. A. Amir, D. Keselman, G. M. Landau, M. Lewenstein, N. Lewenstein, and M. Rodeh. Indexing and dictionary matching with one error. In Proc. 6th WADS, volume 1663 of LNCS, pages 181–92. Springer-Verlag, 1999.

    Google Scholar 

  3. R. A. Baeza-Yates and G. Navarro. A faster algorithm for approximate string matching. In Proc. 7th CPM, volume 1075 of LNCS, pages 1–23. Springer-Verlag, 1996.

    Google Scholar 

  4. R. A. Baeza-Yates and G. Navarro. Multiple approximate string matching. In Proc. 5th WADS, volume 1272 of LNCS, pages 174–84. Springer-Verlag, 1997.

    Google Scholar 

  5. A. L. Buchsbaum, Y. Chen, H. Huang, E. Koutsofios, J. Mocinego, A. Rogers, M. Jenkowsky, and S. Mancoridis. Enterprise navigator: A system for visualizing and analyzing software infrastructures. Technical Report 99.16.1, AT&T Labs-Research, 1999. Submitted for publication.

    Google Scholar 

  6. A. L. Buchsbaum, H. Kaplan, A. Rogers, and J. R. Westbrook. A new, simpler linear-time dominators algorithm. ACM TOPLAS, 20(6):1265–96, 1998.

    Article  Google Scholar 

  7. A. L. Buchsbaum and J. R. Westbrook. Maintaining hierarchical graph views. In Proc. 11th ACM-SIAM SODA, pages 566–75, 2000.

    Google Scholar 

  8. B. Chazelle. A functional approach to data structures and its use in multidimensional searching. SIAM J. 1988.

    Google Scholar 

  9. C. A. Duncan, M. T. Goodrich, and S. Kobourov. Balanced aspect ratio trees and their use for drawing very large graphs. In Proc. GD’ 98, volume 1547 of LNCS, pages 111–24. Springer-Verlag, 1998.

    Google Scholar 

  10. H. Edelsbrunner. A note on dynamic range searching. Bull. EATCS, 15:34–40, 1981.

    Google Scholar 

  11. P. Ferragina, S. Muthukrishnan, and M. de Berg. Multi-method dispatching: A geometric approach with applications to string matching problems. In Proc. 31st ACM STOC, pages 483–91, 1999.

    Google Scholar 

  12. O. Fries, K. Mehlhorn, S. Näher, and A. Tsakalidis. A log log n data structure for three-sided range queries. IPL, 25:269–73, 1987.

    Article  MATH  Google Scholar 

  13. H. N. Gabow. Data structures for weighted matching and nearest common ancestors with linking. In Proc. 1st ACM-SIAM SODA, pages 434–43, 1990.

    Google Scholar 

  14. Z. Galil and R. Giancarlo. Data structures and algorithms for approximate string matching. J. Complexity, 4:33–78, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  15. R. Grossi and J. S. Vitter. Compressed suffix arrays and suffix trees with applications to text indexing and string matching. In Proc. 32nd ACM STOC, pages 397–406, 2000.

    Google Scholar 

  16. D. Harel and R. E. Tarjan. Fast algorithms for finding nearest common ancestors. SIAM J. 1984.

    Google Scholar 

  17. R. Johnson, D. Pearson, and K. Pingali. The program structure tree: Computing control regions in linear time. In Proc. ACM SIGPLAN PLDI’ 94, pages 171–85, 1994.

    Google Scholar 

  18. V. N. Kas’janov. Distinguishing hammocks in a directed graph. Sov. Math. Dokl., 16(2):448–50, 1975.

    Google Scholar 

  19. V. I. Levenshtein. Binary codes capable of correcting deletions, insertions and reversals. Sov. Phys. Dok., 10:707–10, 1966.

    MathSciNet  Google Scholar 

  20. U. Manber and S. Wu. An algorithm for approximate membership checking with application to password security. IPL, 50(4):191–7, 1994.

    Article  MATH  Google Scholar 

  21. E. M. McCreight. A space-economical suffix tree construction algorithm. J. ACM, 23(2):262–72, 1976.

    Article  MATH  MathSciNet  Google Scholar 

  22. R. Muth and U. Manber. Approximate multiple string search. In Proc. 7th CPM, volume 1075 of LNCS, pages 75–86. Springer-Verlag, 1996.

    Google Scholar 

  23. M. H. Overmars. Efficient data structures for range searching on a grid. J. Alg., 9:254–75, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  24. P. A. Pevzner and M. S. Waterman. Multiple filtration and approximate pattern matching. Algorithmica, 12(1/2):135–54, 1995.

    Article  MathSciNet  Google Scholar 

  25. F. P. Preparata, J. S. Vitter, and M. Yvinec. Output-sensitive generation of the perspective view of isothetic parallelepipeds. Algorithmica, 8(4):257–83, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  26. S. C. Sahinalp and U. Vishkin. Efficient approximate and dynamic matching of patterns using a labeling paradigm. In Proc. 37th IEEE FOCS, pages 320–8, 1996.

    Google Scholar 

  27. R. E. Tarjan. Applications of path compression on balanced trees. J. ACM, 26(4):690–715, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  28. P. Weiner. Linear pattern matching algorithms. In Proc. 14th IEEE Symp. on Switch. and Auto. Thy., pages 1–11, 1973.

    Google Scholar 

  29. D. E. Willard. Examining computational geometry, van Emde Boas trees, and hashing from the perspective of the fusion tree. SIAM J. 2000.

    Google Scholar 

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Author information

Authors and Affiliations

  1. AT&T Labs, Shannon Laboratory, 180 Park Ave, Florham Park, NJ, 07932

    Adam L. Buchsbaum

  2. Dept. of Computer Science, Johns Hopkins University, Baltimore, MD, 21218

    Michael T. Goodrich

  3. 20th Century Television, Los Angeles, CA, 90025

    Jeffery R. Westbrook

Authors
  1. Adam L. Buchsbaum
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  2. Michael T. Goodrich
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  3. Jeffery R. Westbrook
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Warwick, Coventry, CV4 7AL, UK

    Mike S. Paterson

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© 2000 Springer-Verlag Berlin Heidelberg

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Buchsbaum, A.L., Goodrich, M.T., Westbrook, J.R. (2000). Range Searching over Tree Cross Products. In: Paterson, M.S. (eds) Algorithms - ESA 2000. ESA 2000. Lecture Notes in Computer Science, vol 1879. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45253-2_12

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  • DOI: https://doi.org/10.1007/3-540-45253-2_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41004-1

  • Online ISBN: 978-3-540-45253-9

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