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A simple balanced search tree with 0(1) worst-case update time

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44431

Fleischer,  Rudolf
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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MPI-I-92-101.pdf
(beliebiger Volltext), 121KB

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Zitation

Fleischer, R.(1992). A simple balanced search tree with 0(1) worst-case update time (MPI-I-92-101). Saarbrücken: Max-Planck-Institut für Informatik.

In this paper we show how a slight modification of $(a,b)$-trees allows us to perform member and neighbor queries in $O(\log n)$ time and updates in $O(1)$ worst-case time (once the position of the inserted or deleted key is known). Our data structure is quite natural and much simpler than previous worst-case optimal solutions. It is based on two techniques : 1) \em{bucketing}, i.e.~storing an ordered list of $2\log n$ keys in each leaf of an $(a,b)$ tree, and \quad 2) \em{lazy splitting}, i.e.~postponing necessary splits of big nodes until we have time to handle them. It can also be used as a finger tree with $O(\log^*n)$ worst-case update time.