# 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…

## 13 Citations

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### A Note on the Size-Sensitive Packing Lemma

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