A hooray for Poisson approximation

Abstract

We give several examples for Poisson approximation of quantities of interest in the analysis of algorithms: the distribution of node depth in a binary search tree, the distribution of the number of losers in an election algorithm and the discounted profile of a binary search tree. A simple and well-known upper bound for the total variation distance between the distribution of a sum of independent Bernoulli variables and the Poisson distribution with the same mean turns out to be very useful in all three cases.

Keywords

• binary search tree
• multiplicity of maxima
• tree profile
• [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds]
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
• [math.math-co] mathematics [math]/combinatorics [math.co]
• [info.info-cg] computer science [cs]/computational geometry [cs.cg]
• [info.info-hc] computer science [cs]/human-computer interaction [cs.hc]