Two Proofs for Shallow Packings
نویسندگان
چکیده
منابع مشابه
Two Proofs for Shallow Packings
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 ...
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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...
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The packing lemma of Haussler states that given a set system (X,R) with bounded VC dimension, if every pair of sets in R have large symmetric difference, then R cannot contain too many sets. Recently it was generalized to the shallow packing lemma, applying to set systems as a function of their shallow-cell complexity. In this paper we present several new results and applications related to pac...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2016
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-016-9824-0