, Volume 1, Issue 1–4, pp 163–191 | Cite as

Fractional cascading: II. Applications

  • Bernard Chazelle
  • Leonidas J. Guibas


This paper presents several applications offractional cascading, a new searching technique which has been described in a companion paper. The applications center around a variety of geometric query problems. Examples include intersecting a polygonal path with a line, slanted range search, orthogonal range search, computing locus functions, and others. Some results on the optimality of fractional cascading, and certain extensions of the technique for retrieving additional information are also included.

Key words

Fractional cascading Iterative search Multiple look-up Binary search B-tree Iterative search Multiple look-up Range query Dynamization of data structures 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [B]
    J. L. Bentley.Multidimensional divide and conquer. Commun. ACM,23, 4 (1880), 214–229.CrossRefMathSciNetGoogle Scholar
  2. [Bsa]
    J. L. Bentley and J. B. Saxe.Decomposable searching problems I: static to dynamic transformations. J. Algorithms,1 (1980), 301–358.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [BS]
    J. L. Bentley and M. I. Shamos.A problem in multivariate statistics: Algorithms, datastructures and applications. Proc. 15th Allerton Conf. Comm., Contr., and Comput. (1977), 193–201.Google Scholar
  4. [BW]
    J. L. Bentley and D. Wood.An Optimal worst-case algorithm for reporting intersections of rectangles. IEEE Trans. Comput.,C-29 (1980), 571–577.CrossRefMathSciNetGoogle Scholar
  5. [Ch1]
    B. Chazelle.Filtering search: A new approach to query-answering. Proc. 24th Ann. Symp. Found. Comput. Sci. (1983), 122–132. To appear in SIAM J. Comput. (1986).Google Scholar
  6. [Ch2]
    B. Chazelle.How to search in history. Inform, and Control (1985).Google Scholar
  7. [Ch3]
    B. Chazelle.A functional approach to data structures and its use in multidimensional searching. Brown Univ. Tech. Rept, CS-85-16, Sept. 1985 (preliminary version in 26th FOCS, 1985).Google Scholar
  8. [CCP]
    B. Chazelle, R. Cole, F. P. Preparata, and C. K. Yap.New upper bounds for neighbor searching. Tech. Rept. CS-84-11 (1984), Brown University, Providence, RI.Google Scholar
  9. [CE]
    B. Chazelle and H. Edelsbrunner.Linear space data structures for a class of range search. To appear in Proc. 2nd ACM Symposium on Computational Geometry, 1986.Google Scholar
  10. [CG]
    B. Chazelle and L. J. Guibas.Visibility and intersection problems in plane geometry. Proc. 1st ACM Symposium on Computational Geometry, Baltimore, MD, June 1985, pp. 135–146.Google Scholar
  11. [CGL]
    B. Chazelle, L. J. Guibas, and D. T. Lee.The power of geometric duality. BIT,25, 1, (1985). Also, in Proc. 24th Ann. Symp. Found. Comp. Sci. (1983), 217–225.CrossRefMathSciNetGoogle Scholar
  12. [Co]
    R. Cole.Searching and storing similar lists. Tech. Report No. 88, Courant Inst., New York University, New York, Oct. 1983. To appear in J. Algorithms.Google Scholar
  13. [CY]
    R. Cole and C. K. Yap.Geometric retrieval problems, Proc. 24th Ann. Symp. Found. Comput. Sci. (1983), 112–121.Google Scholar
  14. [DE]
    D. P. Dobkin and H. Edelsbrunner.Space searching for intersection objects. Proc. 25th Ann. Symp. Found. Comput. Sci. (1984).Google Scholar
  15. [DM]
    D. P. Dobkin and J. I. Munro.Efficient uses of the past. Proc. 21st Ann. Symp. Found. Comput. Sci. (1980), 200–206.Google Scholar
  16. [E]
    H. Edelsbrunner.Intersection problems in computational geometry. Ph.D. Thesis, Tech. Report, Rep. 93, IIG, Univ. Graz, Austria, 1982.Google Scholar
  17. [EGS]
    H. Edelsbrunner, L. J. Guibas, and J. Stolfi.Optimal point location in a monotone subdivision. To appear.Google Scholar
  18. [EH]
    H. Edelsbrunner and F. Huber.Dissecting sets of points in two and three dimensions. Forthcoming technical report, IIG, University of Graz, Austria, 1984.Google Scholar
  19. [EKM]
    H. Edelsbrunner, D. G. Kirkpatrick, and H. A. Maurer.Polygonal intersection search. In-form. Process. Lett.14 (1982), 74–79.zbMATHCrossRefMathSciNetGoogle Scholar
  20. [EW]
    H. Edelsbrunner and E. Welzl.Halfplanar range search in linear space and O(n0.695)query time. Tech. Report, F-111, IIG, University of Graz, Austria 1983.Google Scholar
  21. [GBT]
    H. N. Gabow, J. L. Bentley, and R. E. Tarjan.Scaling and related techniques for geometry problems. Proc. 16th Ann. SIGACT Symp. (1984), 135–143.Google Scholar
  22. [K]
    D. E. Knuth.The art of computer programming, sorting and searching, Vol. 3. Addison-Wesley, Reading, MA, 1973.Google Scholar
  23. [LP]
    D. T. Lee and F. P. Preparata.Location of a point in a planar subdivision and its applications. SIAM J. Comput,6, 3 (1977), 594–606.zbMATHCrossRefMathSciNetGoogle Scholar
  24. [M1]
    E. M. McCreight.Efficient algorithms for enumerating intersecting intervals and rectangles. Tech. Rep., Xerox PARC, CSL-80-9 (June 1980).Google Scholar
  25. [M2]
    E. M. McCreight.Priority search trees. Tech. Rep., Xerox PARC, CSL-81-5 (1981).Google Scholar
  26. [O]
    M. H. Overmars.The design of dynamic data structures. PhD Thesis, University of Utrecht, The Netherlands, 1983.Google Scholar
  27. [T]
    R. E. Tarjan.A class of algorithms which require nonlinear time to maintain disjoint sets. J. Comput. System Sci.,18 (1979), 110–127.zbMATHCrossRefMathSciNetGoogle Scholar
  28. [W]
    D. E. Willard.New data structures for orthogonal queries. To appear in SIAM J. Comput.Google Scholar
  29. [Y]
    F. F. Yao.A 3-space partition and its applications. Proc. 15th Annual SIGACT Symp. (1983), 258–263.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1986

Authors and Affiliations

  • Bernard Chazelle
    • 1
  • Leonidas J. Guibas
    • 2
  1. 1.Brown University and Ecole Normale SupérieureUSA
  2. 2.DEC/SRC and Stanford UniversityUSA

Personalised recommendations