Abstract

. We study binary search trees constructed from Weyl sequences fn`g; n 1, where ` is an irrational and f:g denotes "mod 1". We explore various properties of the structure of these trees, and relate them to the continued fraction expansion of `. If H n is the height of the tree with n nodes when ` is chosen at random and uniformly on [0; 1], then we show that in probability, H n ¸ (12=ß 2 ) log n log log n. Keywords and phrases. Weyl sequence, random number generation, binary search trees, diophantine approximation, random continued fractions, probabilistic analysis, tree height. Authors' address: School of Computer Science, McGill University, 3480 University Street, Montreal, Canada H3A 2K6. The authors' research was sponsored by NSERC Grant A3456 and FCAR Grant 90-ER-0291. Introduction. In this note, we study binary search trees formed by consecutive insertions of numbers f`g; f2`g; f3`g; : : :, where ` 2 (0; 1) is an irrational number, and f:g denotes "mod 1". The sequence in q...

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