The total path length of split trees

Details The total path length of split trees The total path length of split trees

2011-02-12

arxiv.org/abs/1102.2541v2

Mathematics

Probability

Scientific paper

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.

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