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Exponentially Decreasing Number of Operations in Balanced Trees

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Theoretical Computer Science (ICTCS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2202))

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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.

Supported by the IST Programme of the EU (ALCOM-FT) and the Danish SNF.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science Main Campus: Odense University, University of Southern Denmark, Campusvej 55, DK-5230, Odense M, Denmark

    Lars Jacobsen & Kim S. Larsen

Authors
  1. Lars Jacobsen
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  2. Kim S. Larsen
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© 2001 Springer-Verlag Berlin Heidelberg

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Jacobsen, L., Larsen, K.S. (2001). Exponentially Decreasing Number of Operations in Balanced Trees. In: Theoretical Computer Science. ICTCS 2001. Lecture Notes in Computer Science, vol 2202. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45446-2_19

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  • DOI: https://doi.org/10.1007/3-540-45446-2_19

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42672-1

  • Online ISBN: 978-3-540-45446-5

  • eBook Packages: Springer Book Archive

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