Dr. Thomas Sauerwald (Max-Planck-Institut für Informatik, Saarbrücken) will give a guest lecture on Randomized load balancing on networks.

Abstract

We consider the problem of balancing load items (tokens) on networks. Starting with an arbitrary load distribution, we allow in each round nodes to exchange tokens with their neighbors. The goal is to obtain a distribution where all nodes have the same number of tokens. For the continuous case where tokens are arbitrarily divisible, most load balancing schemes correspond to Markov chains whose convergence is fairly well-understood in terms of their spectral gap.

However, in many applications load items cannot be divided arbitrarily often and we need to deal with the discrete case where load is composed of indivisible tokens. In this talk we investigate a natural randomized protocol and demonstrate that there is almost no difference between the discrete and continuous case. Specifically, we show that for any regular network, all nodes have the same number of tokens up to an additive constant in the same number of rounds as in the continuous case.