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Exponentially decreasing number of operations in balanced trees

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Abstract

While many tree-like structures have been proven to support amortized constant number of operations after updates, considerably fewer structures have been proven to support the more general exponentially decreasing number of operations with respect to distance from the update. In addition, all existing proofs of exponentially decreasing operations are tailor-made for specific structures. We provide the first formalization of conditions under which amortized constant number of operations imply exponentially decreasing number of operations. Since our proof is constructive, we obtain the constants involved immediately. Moreover, we develop a number of techniques to improve these constants.

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Authors and Affiliations

  1. Systematic Software Engineering A/S, Aarhus, Denmark

    Lars Jacobsen

  2. Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Campusvej 55, 5230, Odense M, Denmark

    Kim Skak Larsen

Authors
  1. Lars Jacobsen
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  2. Kim Skak Larsen
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Correspondence to Kim Skak Larsen.

Additional information

Supported in part by the Danish Natural Science Research Council (SNF) and in part by the Future and Emerging Technologies programme of the EU under contract number IST-1999-14186 (ALCOM-FT). A preliminary version of this paper appeared in the Seventh Italian Conference on Theoretical Computer Science, Lecture Notes in Computer Science, vol. 2202, pages 293–311, Springer-Verlag, 2001.

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Jacobsen, L., Larsen, K.S. Exponentially decreasing number of operations in balanced trees. Acta Informatica 42, 57–78 (2005). https://doi.org/10.1007/s00236-005-0173-3

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  • DOI: https://doi.org/10.1007/s00236-005-0173-3

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