Constructive Discrepancy Minimization for Convex Sets

@article{Rothvoss2014ConstructiveDM,
  title={Constructive Discrepancy Minimization for Convex Sets},
  author={Thomas Rothvoss},
  journal={2014 IEEE 55th Annual Symposium on Foundations of Computer Science},
  year={2014},
  pages={140-145}
}
  • T. Rothvoss
  • Published 1 April 2014
  • Mathematics
  • 2014 IEEE 55th Annual Symposium on Foundations of Computer Science
A classical theorem of Spencer shows that any set system with n sets and n elements admits a coloring of discrepancy O(√(n)). Recent exciting work of Bansal, Lovett and Meka shows that such colorings can be found in polynomial time. In fact, the Lovett-Meka algorithm finds a half integral point in any "large enough" polytope. However, their algorithm crucially relies on the facet structure and does not apply to general convex sets. We show that for any symmetric convex set K with measure at… 

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