# Noon lecture

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On 05.04.2012 at 12:20 in S6, there is the following noon lecture:

# 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.

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