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European Symposium on Algorithms

ESA 1994: Algorithms — ESA '94 pp 240–253Cite as

Range searching and point location among fat objects

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 855))

Abstract

We present a data structure that can store a set of disjoint fat objects in 2- and 3-space such that point location and bounded-size range searching with arbitrarily shaped regions can be performed efficiently. The structure can deal with either arbitrary (fat) convex objects or non-convex polygonal/polyhedral objects. For dimension d=2,3, the multi-purpose data structure supports point location and range searching queries in time O(logd−1 n) and requires O(n logd−1 n) storage, after O(n logd−1 n log log n) preprocessing. The data structure and query algorithm are rather simple. The results are likely to be extendible in many directions.

Research is supported by the Dutch Organization for Scientific Research (N.W.O.) and by the ESPRIT III BRA Project 7141 (ALCOM II).

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References

  1. P.K. Agarwal and J. Matoušek, On range searching with semialgebraic, Proc. 17th Symp. Mathematical Foundations of Computer Science, Lecture Notes in Computer Science 629 (1992), pp. 1–13.

    Google Scholar 

  2. H. Alt, R. Fleischer, M. Kaufmann, K. Mehlhorn, S. Näher, S. Schirra, and C. Uhrig, Approximate motion planning and the complexity of the boundary of the union of simple geometric figures, Algorithmica8 (1992), pp. 391–406.

    Article  MathSciNet  Google Scholar 

  3. B. Chazelle, Convex partitions of polyhedra: a lower bound and worst-case optimal algorithm, SIAM Journal on Computing13 (1984), pp. 488–507.

    Article  MATH  MathSciNet  Google Scholar 

  4. B. Chazelle, How to search in history, Information and Control64 (1985), pp. 77–99.

    Article  MATH  MathSciNet  Google Scholar 

  5. B. Chazelle and L. Guibas, Fractional cascading I: A data structuring technique, Algorithmica1 (1986), pp. 133–162.

    MathSciNet  Google Scholar 

  6. B. Chazelle, M. Sharir, and E. Welzl, Quasi-optimal upper bounds for simplex range searching and new zone theorems, Algorithmica8 (1992), pp. 407–429.

    Article  MathSciNet  Google Scholar 

  7. B. Chazelle and E. Welzl, Quasi-optimal range searching in spaces of finite VC-dimension, Discrete & Computational Geometry4 (1989), pp. 467–489.

    MathSciNet  Google Scholar 

  8. M.T. Goodrich and R. Tamassia, Dynamic trees and dynamic point location, Proc. 23rd ACM Symp. on Theory of Computing (1991), pp. 523–533.

    Google Scholar 

  9. D. Halperin and M. Overmars, Spheres, molecules, and hidden surface removal, Proc. 10th ACM Symp. on Computational Geometry (1994), pp. 113–122.

    Google Scholar 

  10. M. van Kreveld, New results on data structures in computational geometry, Ph.D. Thesis, Dept. of Computer Science, Utrecht University (1992).

    Google Scholar 

  11. J. Matoušek, Efficient partition trees, Discrete & Computational Geometry8 (1992), pp. 315–334.

    MathSciNet  Google Scholar 

  12. J. Matoušek, Range searching with efficient hierarchical cuttings, Discrete & Computational Geometry10 (1993), pp. 157–182.

    MathSciNet  Google Scholar 

  13. J. Matoušek, J. Pach, M. Sharir, S. Sifrony, and E. Welzl, Fat triangles determine linearly many holes, SIAM Journal on Computing23 (1994), pp. 154–169.

    MathSciNet  Google Scholar 

  14. K. Mehlhorn and S. Näher, Dynamic fractional cascading, Algorithmica5 (1990), pp. 215–241.

    Article  MathSciNet  Google Scholar 

  15. M.H. Overmars, Point location in fat subdivisions, Information Processing Letters44 (1992), pp. 261–265.

    Article  MATH  MathSciNet  Google Scholar 

  16. M.H. Overmars and A.F. van der Stappen, Range searching and point location among fat objects, in preparation.

    Google Scholar 

  17. F.P. Preparata and M.I. Shamos, Computational geometry: an introduction, Springer Verlag, New York (1985).

    Google Scholar 

  18. F.P. Preparata and R. Tamassia, Efficient spatial point location, Proc. 1st Workshop on Algorithms and Data Structures, Lecture Notes in Computer Science 382 (1989), pp. 3–11.

    Google Scholar 

  19. A.F. van der Stappen, D. Halperin, M.H. Overmars, The complexity of the free space for a robot moving amidst fat obstacles, Computational Geometry, Theory and Applications3 (1993), pp. 353–373.

    MathSciNet  Google Scholar 

  20. A.F. van der Stappen and M.H. Overmars, Motion planning amidst fat obstacles, Proc. 10th ACM Symp. on Computational Geometry (1994), pp. 31–40.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, Utrecht University, P.O. Box 80.089, 3508, TB Utrecht, The Netherlands

    Mark H. Overmars & A. Frank van der Stappen

Authors
  1. Mark H. Overmars
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  2. A. Frank van der Stappen
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Jan van Leeuwen

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© 1994 Springer-Verlag Berlin Heidelberg

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Overmars, M.H., van der Stappen, A.F. (1994). Range searching and point location among fat objects. In: van Leeuwen, J. (eds) Algorithms — ESA '94. ESA 1994. Lecture Notes in Computer Science, vol 855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0049412

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  • DOI: https://doi.org/10.1007/BFb0049412

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58434-6

  • Online ISBN: 978-3-540-48794-4

  • eBook Packages: Springer Book Archive

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