Abstract
A set of vertices is shattered in a hypergraph if any of its subsets is obtained as the intersection of an edge with the set. The VC dimension is the size of the largest shattered subset. Under the binomial model of k-uniform random hypergraphs, the threshold function for the VC dimension to be larger than a given integer is obtained. The same is done for the testing dimension, which is the largest integer d such that all sets of cardinality d are shattered.
Original language | English |
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Pages (from-to) | 564-572 |
Number of pages | 9 |
Journal | Random Structures and Algorithms |
Volume | 30 |
Issue number | 4 |
DOIs | |
State | Published - 1 Jul 2007 |
Keywords
- Random hypergraph
- Testing dimension
- Threshold
- Vapnik-Chervonenkis
ASJC Scopus subject areas
- Software
- General Mathematics
- Computer Graphics and Computer-Aided Design
- Applied Mathematics