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A dynamic fixed windowing problem

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Abstract

Given a point set in the plane and a fixed planar region (window) a window query consists of enumerating the points in a translate of the region. A recently presented result demonstrates that there is astatic data structure, of optimal size, that solves window queries for convex regions in optimal time. We give a data structure, of optimal size, that not only supports window queries in optimal time for, possibly nonconvex, polygonal windows, but also allows updating of the point set in optimal time.

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References

  1. M. D. Atkinson, J.-R. Sack, N. Santoro, and Th. Strothotte. Min-max heaps and generalized priority queues.Communications of the ACM,29:996–1000, 1986.

    Article  MATH  Google Scholar 

  2. R. Bayer. Symmetric binary B-trees: data structure and maintenance algorithms.Acta Informatica,1:290–306, 1972.

    Article  MATH  MathSciNet  Google Scholar 

  3. J. L. Bentley and J. B. Saxe. Decomposable searching problems I: static-to-dynamic transformation.Journal of Algorithms,1:301–358, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  4. B. Chazelle and H. Edelsbrunner. Optimal solutions for a class of point retrieval problems. InProceedings of the 12th International Colloquium on Automata, Languages, and Programming, pp. 80–89, 1985.

  5. R. H. Güiting. Dynamic C-oriented polygon intersection searching.Information and Control,63:143–163, 1984.

    Article  MathSciNet  Google Scholar 

  6. E. M. McCreight. Priority search trees.SIAM Journal on Computing,14:257–276, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  7. H. J. Olivié. A new class of balanced binary search trees.RAIRO Informatique théoretique,16:51–71, 1982.

    MATH  Google Scholar 

  8. M. H. Overmars.The Design of Dynamic Data Structures. Springer-Verlag, New York, 1983.

    MATH  Google Scholar 

  9. M. H. Overmars and J. van Leeuwen. Two general methods for dynamizing decomposable searching problems.Information Processing Letters,12:168–173, 1981.

    Article  MATH  Google Scholar 

  10. R. E. Tarjan. Updating balanced search trees inO(1) rotations.Information Processing Letters,16:253–257, 1983.

    Article  MATH  MathSciNet  Google Scholar 

  11. J. van Leeuwen and D. Wood. Dynamization of decomposable searching problems.Information Processing Letters,10:51–56, 1980.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institut für Informatik, Universität Freiburg, Rheinstrasse 10-12, D-7800, Freiburg, Federal Republic of Germany

    Rolf Klein, Otto Nurmi & Thomas Ottmann

  2. Data Structuring Group, Department of Computer Science, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Derick Wood

Authors
  1. Rolf Klein
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  2. Otto Nurmi
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  3. Thomas Ottmann
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  4. Derick Wood
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Additional information

Communicated by Kurt Mehlhorn.

This work was partially supported by Grant No. O164/4-2 from the Deutsche Forschungsgemein-schaft and partially under a Natural Sciences and Engineering Research Council of Canada Grant No. A-5692.

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Klein, R., Nurmi, O., Ottmann, T. et al. A dynamic fixed windowing problem. Algorithmica 4, 535–550 (1989). https://doi.org/10.1007/BF01553907

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  • DOI: https://doi.org/10.1007/BF01553907

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