@inproceedings{e9210973fcae4893a2dc1786282de014,

title = "Explicit construction of a small epsilon-net for linear threshold functions",

abstract = "We give explicit constructions of epsilon nets for linear threshold functions on the binary cube and on the unit sphere. The size of the constructed nets is polynomial in the dimension n and in 1/ε . To the best of our knowledge no such constructions were previously known. Our results match, up to the exponent of the polynomial, the bounds that are achieved by probabilistic arguments. As a corollary we also construct subsets of the binary cube that have size polynomial in n and covering radius of n/2 - c√n log n, for any constant c. This improves upon the well known construction of dual BCH codes that only guarantee covering radius of n/2 - c√n.",

keywords = "Epsilon-net, Explicit construction, Linear threshold function",

author = "Yuval Rabani and Amir Shpilka",

year = "2009",

doi = "10.1145/1536414.1536502",

language = "American English",

isbn = "9781605585062",

series = "Proceedings of the Annual ACM Symposium on Theory of Computing",

pages = "649--658",

booktitle = "STOC'09 - Proceedings of the 2009 ACM International Symposium on Theory of Computing",

note = "41st Annual ACM Symposium on Theory of Computing, STOC '09 ; Conference date: 31-05-2009 Through 02-06-2009",

}