Article

Algorithmica

, Volume 1, Issue 1, pp 133-162

Fractional cascading: I. A data structuring technique

  • Bernard ChazelleAffiliated withBrown University and Ecole Normale Supérieure
  • , Leonidas J. GuibasAffiliated withDEC/SRC and Stanford University

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Abstract

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.

Key words

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