The total path length of split trees

11 years 1 months ago
The total path length of split trees
We consider the model of random trees introduced by Devroye [SIAM J Comput 28, 409– 432, 1998]. The model encompasses many important randomized algorithms and data structures. The pieces of data (items) are stored in a randomized fashion in the nodes of a tree. The total path length (sum of depths of the items) is a natural measure of the efficiency of the algorithm/data structure. Using renewal theory, we prove convergence in distribution of the total path length towards a distribution characterized uniquely by a fixed point equation. Our result covers, using a unified approach, many data structures such as binary search trees, m-ary search trees, quad trees, median-of-(2k + 1) trees, and simplex trees.
Nicolas Broutin, Cecilia Holmgren
Added 28 May 2011
Updated 28 May 2011
Type Journal
Year 2011
Where CORR
Authors Nicolas Broutin, Cecilia Holmgren
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