Coalescing Balls and Bins

Jarett Schwartz

Abstract

We analyze a process, motivated by a distributed algorithm from a system at Microsoft Research where n singleton bins merge until we have d bins. After relating this process to the Kingman Coalescent process from evolutionary biology and random compositions with d parts, we find a closed form for the expected maximum bin size for constant d, as n tends to infinity. Then, we present results for various choices of d = f(n). If time allows, we will propose problems relating to extensions to this process ("waking" bins, power of two choices, etc.).

This is joint work with Siddhartha Sen.