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Probability Theory and Related Fields

, Volume 162, Issue 3–4, pp 679–705 | Cite as

Sparse covers for sums of indicators

  • Constantinos Daskalakis
  • Christos Papadimitriou
Article

Abstract

For all \(n, \epsilon >0\), we show that the set of Poisson Binomial distributions on \(n\) variables admits a proper \(\epsilon \)-cover in total variation distance of size \(n^2+n \cdot (1/\epsilon )^{O(\log ^2 (1/\epsilon ))}\), 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.

Mathematics Subject Classification

60F99 

Notes

Acknowledgments

We thank the anonymous reviewer for comments that helped improve the presentation.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Constantinos Daskalakis
    • 1
  • Christos Papadimitriou
    • 2
  1. 1.EECS and CSAILMITCambridgeUSA
  2. 2.Computer ScienceU.C. BerkeleyBerkeleyUSA

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