Average depth in a binary search tree with repeated keys

Margaret Archibald 1 Julien Clément 2, 3
2 Equipe AMACC - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
Abstract : Random sequences from alphabet $\{1, \ldots,r\}$ are examined where repeated letters are allowed. Binary search trees are formed from these, and the average left-going depth of the first $1$ is found. Next, the right-going depth of the first $r$ is examined, and finally a merge (or 'shuffle') operator is used to obtain the average depth of an arbitrary node, which can be expressed in terms of the left-going and right-going depths. The variance of each of these parameters is also found.
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Communication dans un congrès
Chassaing, Philippe and others. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, pp.309-320, 2006, DMTCS Proceedings
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Margaret Archibald, Julien Clément. Average depth in a binary search tree with repeated keys. Chassaing, Philippe and others. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, pp.309-320, 2006, DMTCS Proceedings. 〈hal-01184700〉

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