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- W2220975065 abstract "Given a finite n-element set X, a family of subsets F⊂2X is said to separate X if any two elements of X are separated by at least one member of F. It is shown that if |F|>2n−1, then one can select ⌈logn⌉+1 members of F that separate X. If |F|≥α2n for some 0<α<1/2, then logn+O(log1αloglog1α) members of F are always sufficient to separate all pairs of elements of X that are separated by some member of F. This result is generalized to simultaneous separation in several sets. Analogous questions on separation by families of bounded Vapnik–Chervonenkis dimension and separation of point sets in Rd by convex sets are also considered." @default.
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- W2220975065 date "2016-11-01" @default.
- W2220975065 modified "2023-10-11" @default.
- W2220975065 title "Separation with restricted families of sets" @default.
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- W2220975065 doi "https://doi.org/10.1016/j.jcta.2016.06.002" @default.
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