Poisson approximations for functionals of random trees
Article first published online: 7 DEC 1998
Copyright © 1996 John Wiley & Sons, Inc.
Random Structures & Algorithms
Volume 9, Issue 1-2, pages 79–92, August - September 1996
How to Cite
Dobrow, R. P. and Smythe, R. T. (1996), Poisson approximations for functionals of random trees. Random Struct. Alg., 9: 79–92. doi: 10.1002/(SICI)1098-2418(199608/09)9:1/2<79::AID-RSA5>3.0.CO;2-8
- Issue published online: 7 DEC 1998
- Article first published online: 7 DEC 1998
- Manuscript Accepted: 2 OCT 1995
- Manuscript Received: 23 JUN 1995
- Poisson approximation;
- binary search trees;
- increasing trees;
- recursive trees
We use Poisson approximation techniques for sums of indicator random variables to derive explicit error bounds and central limit theorems for several functionals of random trees. In particular, we consider (i) the number of comparisons for successful and unsuccessful search in a binary search tree and (ii) internode distances in increasing trees. The Poisson approximation setting is shown to be a natural and fairly simple framework for deriving asymptotic results. © 1996 John Wiley & Sons, Inc.