Exponentially Decreasing Number of Operations in Balanced Trees

  • Lars Jacobsen
  • Kim S. Larsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2202)


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.


Search Tree Internal Node Local Rule Layer Function Balance Tree 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Lars Jacobsen
    • 1
  • Kim S. Larsen
    • 1
  1. 1.Department of Mathematics and Computer Science Main Campus: Odense UniversityUniversity of Southern DenmarkOdense MDenmark

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