Optimal Stopping in the Balls-and-Bins Problem

Balanced Allocations: Balls-into-Bins Revisited and Chains-into-Bins

The study of balls-into-bins games or occupancy problems has a long history since these processes can be used to translate realistic problems into mathematical ones in a natural way. In general, the goal of a balls-into-bins game is to allocate a set of independent objects (tasks, jobs, balls) to a set of resources (servers, bins, urns) and, thereby, to minimize the maximum load. In this paper ...

Balls into Bins Made Faster

Balls-into-bins games describe in an abstract setting several multiple-choice scenarios, and allow for a systematic and unified theoretical treatment. In the process that we consider, there are n bins, initially empty, and m = bcnc balls. Each ball chooses independently and uniformly at random k ≥ 3 bins. We are looking for an allocation such that each ball is placed into one of its chosen bins...

The forgetfulness of balls and bins

The Problem of Optimal Stopping

The problem of Optimal Stopping is of fundamental importance for sequential analysis, for the detection of signals in a background of noise, and also for pricing American-type options in the modern theory of finance. We shall review in this talk two relatively recent approaches to this problem: the deterministic or “pathwise” approach of Davis & Karatzas (1994), and the “integral representation...

Simple gossiping with balls and bins

Recent research suggests decentralised probabilistic protocols on support for multipeer communication. The protocols scale well and impose an even load on the system. They provide statistical guarantees for the reliability, i.e. an information sent from an arbitrary source will reach all its destinations. Analysing the reliability is based on modelling the propagation of events as an epidemic p...