CaltechAUTHORS
Published June 2001 | Version public
Book Section - Chapter Metadata-only

On the Complexity of Approximating the VC dimension

Creators

Abstract

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: Σ_3^p-hard to approximate to within a factor 2-ε for any ε>0; approximable in AM to within a factor 2; and AM-hard to approximate to within a factor N_ε for some constant ε>0. To obtain the Σ_3^p-hardness results we solve a randomness extraction problem using list-decodable binary codes; for the positive results we utilize the Sauer-Shelah(-Perles) Lemma. The exact value of ε in the AM-hardness result depends on the degree achievable by explicit disperser constructions.

Additional Information

© 2001 IEEE. Date of Current Version: 07 August 2002. We thank Gil Kalai for helpful discussions and Adam Smith for a useful reference.

Additional details

Identifiers

Eprint ID
27860
DOI
10.1109/CCC.2001.933889
Resolver ID
CaltechAUTHORS:20111118-115638180

Dates

Created
2011-11-21
Created from EPrint's datestamp field
Updated
2021-11-09
Created from EPrint's last_modified field

Caltech Custom Metadata

Series Name
Annual IEEE Conference on Computational Complexity
Other Numbering System Name
INSPEC Accession Number
Other Numbering System Identifier
6998461