, Volume 5, Issue 1–4, pp 215–241 | Cite as

Dynamic fractional cascading

  • Kurt Mehlhorn
  • Stefan Näher


The problem of searching for a key in many ordered lists arises frequently in computational geometry. Chazelle and Guibas recently introduced fractional cascading as a general technique for solving this type of problem. In this paper we show that fractional cascading also supports insertions into and deletions from the lists efficiently. More specifically, we show that a search for a key inn lists takes timeO(logN +n log logN) and an insertion or deletion takes timeO(log logN). HereN is the total size of all lists. If only insertions or deletions have to be supported theO(log logN) factor reduces toO(1). As an application we show that queries, insertions, and deletions into segment trees or range trees can be supported in timeO(logn log logn), whenn is the number of segments (points).

Key words

Computational geometry Linear lists Dynamic data structures Amortized complexity 


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Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • Kurt Mehlhorn
    • 1
  • Stefan Näher
    • 1
  1. 1.Universität des SaarlandesSaarbrückenFederal Republic of Germany

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