Two Proofs for Shallow Packings

@inproceedings{Dutta2015TwoPF,
  title={Two Proofs for Shallow Packings},
  author={Kunal Dutta and Esther Ezra and Arijit Ghosh},
  booktitle={Symposium on Computational Geometry},
  year={2015}
}
We refine the bound on the packing number, originally shown by Haussler, for shallow geometric set systems. Specifically, let V be a finite set system defined over an n-point set X; we view V as a set of indicator vectors over the n-dimensional unit cube. A δ-separated set of V is a subcollection W, s.t. the Hamming distance between each pair u,v ∈W is greater than δ, where δ > 0 is an integer parameter. The δ-packing number is then defined as the cardinality of a largest δ-separated… CONTINUE READING