Fractional cascading: I. A data structuring technique


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.

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Additional information

The first author was supported in part by NSF grants MCS 83-03925 and the Office of Naval Research and the Defense Advanced Research Projects Agency under contract N00014-83-K-0146 and ARPA Order No. 4786. Part of this work was done while the second author was employed by the Xerox Palo Alto Research Center.

Communicated by C. K. Wong.

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Chazelle, B., Guibas, L.J. Fractional cascading: I. A data structuring technique. Algorithmica 1, 133–162 (1986).

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Key words

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