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2009
ACM

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

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Explicit construction of a small epsilon-net for linear threshold functions
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 . 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. Computer Science Department, Technion, Haifa 32000, Israel. Email: rabani,shpilka@cs.technion.ac.il.
Yuval Rabani, Amir Shpilka
Added 23 Nov 2009
Updated 23 Nov 2009
Type Conference
Year 2009
Where STOC
Authors Yuval Rabani, Amir Shpilka
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