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A New Randomized Data Structure for the 1 1/2-dimensional Range Query Problem

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2563))

Abstract

We propose RPST, a randomized data structure for the 11/2-dimensional range query problem, based on a version of Skip Lists, as an alternative to solutions that use deterministic height balanced trees. Our scheme exhibits, with high probability, logarithmic, output-sensitive search time, expected logarithmic update time, expected constant reconstruction time and linear space overhead with high probability.

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References

  1. Bentley J. L., Wood D.: “An Optimal Worst-Case Algorithm for Reporting Intersections of Rectangles”, IEEE Transactions on Computers, Vol.29, No.7, pp.571–577, 1980.

    Article  MathSciNet  Google Scholar 

  2. de Berg M., van Kreveld M., Overmars M. and Schwarzkopf O.: “Computational Geometry: Algorithms and Applications”, Springer, Berlin, 2000. 440, 441

    MATH  Google Scholar 

  3. Bozanis P. and Manolopoulos Y.: “DSL: Accommodating Skip Lists in the SDDS Model”, Proceedings 3rd Workshop on Distributed Data and Structures (WDAS’2000), pp.1–9, L’Aquila, Italy, July 2000. 443

    Google Scholar 

  4. Hanson E. N. and Johnson, T.: “The Interval Skip List: a Data Structure for Finding all Intervals that Overlap a Point”, Proceedings 2nd Workshop on Algorithms and Data Structures (WADS’91), pp.153–164, Ottawa, Canada, August 1991. 440

    Google Scholar 

  5. Huddleston S. and Mehlhorn K.: “A New Representation for Linear Lists”, Acta Informatica, Vol.17, pp.157–184, 1982. 444

    Article  MATH  MathSciNet  Google Scholar 

  6. McCreight E. M.: “Priority Search Trees”, SIAM Journal on Computing, Vol.14, pp.257–276, 1985. 440

    Article  MATH  MathSciNet  Google Scholar 

  7. Mehlhorn K.: “Data Structures & Algorithms, Vol. 3: Multidimensional Searching and Computational Geometry”, Springer, Berlin, 1984. 440, 441, 442, 451

    Google Scholar 

  8. Mulmuley K.: “Computational Geometry: an introduction Through Randomized Algorithms”, Prentice-Hall, Englewood Cliffs, NJ, 1994. 443, 450

    Google Scholar 

  9. Papadakis T.: “Skip Lists and Probabilistic Analysis of Algorithms”, Ph.D. Thesis, University of Waterloo, May 1993. 442

    Google Scholar 

  10. Pugh W.: “A Skip List CookBook”, Technical Report CS-TR-2286, Department of Computer Science, University of Maryland at College Park, July 1989. 442

    Google Scholar 

  11. Pugh W.: “Skip Lists: a Probabilistic Alternative to Balanced Trees”, Communications of the ACM, Vol.33, pp.668–676, 1990. 442

    Article  Google Scholar 

  12. Seidel R. and Aragon C. R.: “Randomized Search Trees”, Algorithmica, Vol.16, pp.464–497, 1996. 443

    Google Scholar 

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© 2003 Springer-Verlag Berlin Heidelberg

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Bozanis, P. (2003). A New Randomized Data Structure for the 1 1/2-dimensional Range Query Problem. In: Manolopoulos, Y., Evripidou, S., Kakas, A.C. (eds) Advances in Informatics. PCI 2001. Lecture Notes in Computer Science, vol 2563. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-38076-0_28

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  • DOI: https://doi.org/10.1007/3-540-38076-0_28

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07544-8

  • Online ISBN: 978-3-540-38076-4

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