TY - GEN

T1 - Explicit construction of a small epsilon-net for linear threshold functions

AU - Rabani, Yuval

AU - Shpilka, Amir

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - Epsilon-net

KW - Explicit construction

KW - Linear threshold function

UR - http://www.scopus.com/inward/record.url?scp=70350694417&partnerID=8YFLogxK

U2 - 10.1145/1536414.1536502

DO - 10.1145/1536414.1536502

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AN - SCOPUS:70350694417

SN - 9781605585062

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 649

EP - 658

BT - STOC'09 - Proceedings of the 2009 ACM International Symposium on Theory of Computing

T2 - 41st Annual ACM Symposium on Theory of Computing, STOC '09

Y2 - 31 May 2009 through 2 June 2009

ER -