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On the internal path length of d-dimensional quad trees

✍ Scribed by Ralph Neininger; Ludger Rüschendorf

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
241 KB
Volume
15
Category
Article
ISSN
1042-9832

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✦ Synopsis

It is proved that the internal path length of a d-dimensional quad tree after normalization converges in distribution. The limiting distribution is characterized as a fixed point of a random affine operator. We obtain convergence of all moments and of the Laplace transforms. The moments of the limiting distribution can be evaluated from the recursion and lead to first order asymptotics for the moments of the internal path lengths. The analysis is based on the contraction method. In the final part of the paper we state similar results for general split tree models if the expectation of the path length has a similar expansion as in the case of quad trees. This applies in particular to the m-ary search trees.

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