The total path length of split trees

Nicolas Broutin (1, 2) , Cecilia Holmgren (2)

1 RAP - Networks, Algorithms and Probabilities
2 ALGORITHMS - Algorithms

We consider the model of random trees introduced by Devroye [SIAM J. Comput. 28 (1999) 409-432]. 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 toward 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.

Domaines: Algorithme et structure de données [cs.DS]; Probabilités [math.PR]; Combinatoire [math.CO]

Nicolas Broutin, Cecilia Holmgren. The total path length of split trees. The Annals of Applied Probability, 2012, 22 (5), pp.1745-1777. ⟨10.1214/11-AAP812⟩. ⟨hal-00773367⟩