- Al.Alon, N., Expanders, sorting in rounds and superconcentrators of limited depth, in "Proc. 17th ACM Sump. on Theory of Coaput." (1985) 98-102. Google ScholarDigital Library
- A2.Al.on, N., Eigenvalues, geometric expanders, sorting in rounds and Ramsey theory, Combinatorics 6 (1986) 207-219. Google ScholarDigital Library
- F.Yredman, M. L., Lower bounds on the complexity of some optimal dstostructures, SIAW J. Cornput. 1C (l!Ml) l-10.Google Scholar
- H.Hall, M.Jr., Combinatorial Theory, Wiley and Sons, New York, London (1967).Google Scholar
- HW.Haussler, D. and Welzl, Is., Bpsilonriots and simplex range search, Discrete and Conput. Geor., to appear.Google Scholar
- L.Lovasz, L., Combinatorial Problems and Exercises, North-Holland, Amsterdam, New York, Oxford (1979).Google Scholar
- S.Sauer, N., On the density of families of sets, J. Combin. Theory Ser. A 13 (1972) 145-147.Google ScholarCross Ref
- VC.Vapnik, V.N. and Chervonenkis', A.YA., On the uniform convergence of relative frequencies of events to their probabilities, Theory Probab. Rpp.1. 16 (1971) 164-280.Google Scholar
- W.Willard, D., Polygon retrieval, SIAM .I. Cornput. 11 (1982) 149-165.Google ScholarCross Ref
- YY.Yaoi A. and Yao, F.) A general approach to d-dfmensional georetric qucrias, in "Proc. 17th ACM Symp. on Theory of Comput." (1985) 163-169. Google ScholarDigital Library
Index Terms
- Partitioning and geometric embedding of range spaces of finite Vapnik-Chervonenkis dimension
Recommendations
Learnability and the Vapnik-Chervonenkis dimension
Valiant's learnability model is extended to learning classes of concepts defined by regions in Euclidean space En. The methods in this paper lead to a unified treatment of some of Valiant's results, along with previous results on distribution-free ...
Embedding metric spaces in their intrinsic dimension
SODA '08: Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithmsA fundamental question of metric embedding is whether the metric dimension of a metric space is related to its intrinsic dimension. That is whether the dimension in which it can be embedded in some real normed space is implied by the intrinsic dimension ...
Dot products in F q 3 and the Vapnik-Chervonenkis dimension
AbstractGiven a set E ⊂ F q 3, where F q is the field with q elements. Consider a set of “classifiers” H t 3 ( E ) = { h y : y ∈ E }, where h y ( x ) = 1 if x ⋅ y = t, x ∈ E, and 0 otherwise. We are going to prove that if | E | ≥ C q 11 4, ...
Comments