Fractional cascading: I. A data structuring technique
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
In computational geometry many search problems and range queries can be solved by performing an iterative search for the same key in separate ordered lists. In this paper we show that, if these ordered lists can be put in a one-to-one correspondence with the nodes of a graph of degreed so that the iterative search always proceeds along edges of that graph, then we can do much better than the obvious sequence of binary searches. Without expanding the storage by more than a constant factor, we can build a data-structure, called afractional cascading structure, in which all original searches after the first can be carried out at only logd extra cost per search. Several results related to the dynamization of this structure are also presented. A companion paper gives numerous applications of this technique to geometric problems.
- J. L. Bentley and J. B. Saxe.Decomposable searching problems I: static to dynamic transformations. J. Algorithms, 1 (1980), 301–358. CrossRef
- P. van Emde Boas, B. Kaas and E. Zijlstra.Design and implementation of an efficient priority queue. Math. Syst. Theory,10 (1977), 99–127. CrossRef
- B. Chazelle.Filtering search: A new approach to query-answering. Proc. 24th Ann. Symp. Found. Comp. Sci. (1983), pp. 122–132. To appear in SIAM J. Comput. (1986).
- B. Chazelle and L. J. Guibas.Fractional cascading II: applications. To appear in Algorithmica (1986).
- R. Cole.Searching and storing similar lists. Tech. Report No. 88, Courant Inst., New York University, New York, Oct. 1983. To apper in J. Algorithms.
- O. Fries, K. Mehlhorn, and St. Näher.Dynamization of geometric data structures. Proc. 1st ACM Computational Geometry Symposium, 1985, pp. 168–176.
- H. Edelsbrunner, L. J. Guibas, and J. Stolfi.Optimal point location in a monotone subdivision. To appear in SIAM J. Comput. Also DEC/SRC Research Report No. 2, 1984.
- H. Imai and T. Asano.Dynamic segment intersection search with applications, Proc. of 25th FOCS Sumposium, 1984, pp. 393–402.
- H. N. Gabow and R. E. Tarjan.A linear-time algorithm for a special case of disjoint set union. Proc. of 24th FOCS Symposium, 1983, pp. 246–251.
- M. H. Overmars.The design of dynamic data structures. PhD Thesis, University of Utrecht, The Netherlands, 1983.
- R. E. Tarjan.Amortized computational complexity. SIAM J. Alg. Disc. Meth.,6 (2) (April 1985), 306–318. CrossRef
- V. K. Vaishani and D. Wood.Rectilinear line segment intersection, layered segment trees, and dynamization. J. Algorithms,3 (1982), 160–176. CrossRef
- Fractional cascading: I. A data structuring technique
Volume 1, Issue 1-4 , pp 133-162
- Cover Date
- Print ISSN
- Online ISSN
- Additional Links
- Binary search
- Iterative search
- Multiple look-up
- Range query
- Dynamization of data structures
- Industry Sectors