Sparse covers for sums of indicators

Abstract

For all n, ε > 0), we show that the set of Poisson Binomial distributions on n variables admits a proper ε-cover in total variation distance of size n[superscript 2] + n · (1/ε)[superscript O(log[superscript 2] (1/ε)), which can also be computed in polynomial time. We discuss the implications of our construction for approximation algorithms and the computation of approximate Nash equilibria in anonymous games.