Two Proofs for Shallow Packings

@article{Dutta2015TwoPF,
  title={Two Proofs for Shallow Packings},
  author={Kunal Dutta and Esther Ezra and Arijit Ghosh},
  journal={Discrete \& Computational Geometry},
  year={2015},
  volume={56},
  pages={910-939}
}
We refine the bound on the packing number, originally shown by Haussler, for shallow geometric set systems. Specifically, let $$\mathcal {V}$$V be a finite set system defined over an n-point set X; we view $$\mathcal {V}$$V as a set of indicator vectors over the n-dimensional unit cube. A $$\delta $$δ-separated set of $$\mathcal {V}$$V is a subcollection $$\mathcal {W}$$W, s.t. the Hamming distance between each pair $$\mathbf{u}, \mathbf{v}\in \mathcal {W}$$u,v∈W is greater than $$\delta… 

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