Unbalanced Allocations

We consider the unbalanced allocation of $m$ balls into $n$ bins by a randomized algorithm using the "power of two choices". For each ball, we select a set of bins at random, then place the ball in the fullest bin within the set. Applications of this generic algorithm range from cost minimization to condensed matter physics. In this paper, we analyze the distribution of the bin loads produced by this algorithm, considering, for example, largest and smallest loads, loads of subsets of the bins, and the likelihood of bins having equal loads

News Recommender Systems with Feedback

The focus of present research is widely used news recommendation techniques such as “most popular” or “most e-mailed”. In this paper we have introduced an alternative way of recommendation based on feedback. Various notable properties of the feedback based recommendation technique have been also discussed. Through simulation model we show that the recommendation technique used in the present research allows implementers to have a flexibility to make a balance between accuracy and distortion. Analytical results have been established in a special case of two articles using the formulation based on generalized urn models. Finally, we show that news recommender systems can be also studied through two armed bandit algorithms

A Scaling Result for Explosive Processes

We consider the asymptotic behavior of the following model: balls are sequentially thrown into bins so that the probability that a bin with n balls obtains the next ball is proportional to f(n) for some function f . A commonly studied case where there are two bins and f(n) = n for p > 1. In this case, one of the two bins eventually obtains a monopoly, in the sense that it obtains all balls thrown past some point. This model is motivated by the phenomenon of positive feedback, where the \rich get richer." We derive a simple asymptotic expression for the probability that bin 1 obtains a monopoly when bin 1 starts with x balls and bin 2 starts with y balls for the case f(n) = n . We then demonstrate the eectiveness of this approximation with some examples and demonstrate how it generalizes to a wide class of functions f