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COCO
2001
Springer

On the Complexity of Approximating the VC Dimension

10 years 2 months ago
On the Complexity of Approximating the VC Dimension
We study the complexity of approximating the VC dimension of a collection of sets, when the sets are encoded succinctly by a small circuit. We show that this problem is • Σp 3-hard to approximate to within a factor 2− for any > 0, • approximable in AM to within a factor 2, and • AM-hard to approximate to within a factor N for some constant > 0. To obtain the Σp 3-hardness result we solve a randomness extraction problem using list-decodable binary codes; for the positive result we utilize the Sauer-Shelah(-Perles) Lemma. The exact value of in the AM-hardness result depends on the degree achievable by explicit disperser constructions.
Elchanan Mossel, Christopher Umans
Added 28 Jul 2010
Updated 28 Jul 2010
Type Conference
Year 2001
Where COCO
Authors Elchanan Mossel, Christopher Umans
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