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One-sided variations on interval trees. (English) Zbl 1043.05036

Summary: The binary interval tree is a random structure that underlies interval division and parking problems. Five incomplete one-sided variants of binary interval trees are considered, providing additional flavors and variations on the main applications. The size of each variant is studied, and a Gaussian tendency is proved in each case via an analytic approach. Differential equations on half scale and delayed differential equations arise and can be solved asymptotically by local expansions and Tauberian theorems. Unlike the binary case, in an incomplete interval tree the size determines most other parameters of interest, such as the height or the internal path length.

MSC:

05C05 Trees
60F05 Central limit and other weak theorems
34C60 Qualitative investigation and simulation of ordinary differential equation models
05C80 Random graphs (graph-theoretic aspects)
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