Constructive Algorithms for Discrepancy Minimization

@article{Bansal2010ConstructiveAF,
  title={Constructive Algorithms for Discrepancy Minimization},
  author={Nikhil Bansal},
  journal={2010 IEEE 51st Annual Symposium on Foundations of Computer Science},
  year={2010},
  pages={3-10}
}
Given a set system $(V,\mathcal{S})$, $V=\{1,\ldots,n\}$ and $\mathcal{S}=\{S_1,\ldots,S_m\}$, the minimum discrepancy problem is to find a 2-coloring $\mathcal{X}:V \right arrow \{-1,+1\}$, such that each set is colored as evenly as possible, i.e. find $\mathcal{X}$ to minimize $\max_{j \in [m]} \left|\sum_{i \in S_j} \mathcal{X}(i)\right|$. In this paper we give the first polynomial time algorithms for discrepancy minimization that achieve bounds similar to those known existentially using the… CONTINUE READING
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