Acta Informatica

, Volume 42, Issue 1, pp 57–78 | Cite as

Exponentially decreasing number of operations in balanced trees

  • Lars Jacobsen
  • Kim Skak Larsen
Original Paper


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.


Information System Operating System Data Structure Communication Network Information Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Systematic Software Engineering A/SAarhusDenmark
  2. 2.Department of Mathematics and Computer ScienceUniversity of Southern DenmarkOdense MDenmark

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