Forbidding extreme points from the 0− 1 hypercube
نویسندگان
چکیده
Let B be the set of n-dimensional binary vectors and let V be a subset of m of its elements. We give an extended formulation of the convex hull of B \ V which is polynomial in n and m. In developing this result, we give a two-sided extension of the result in [3] for knapsack sets with superincreasing coefficients.
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Comment on "Volumes spanned by random points in the hypercube"
Consider the hypercube [0, 1]n in R. This has 2n vertices and volume 1. Pick N = N(n) vertices independently at random, form their convex hull, and let Vn be its expected volume. How large should N(n) be to pick up significant volume ? Let κ = 2/ √ e ≈ 1.213, and let 2 > 0. We shall show that, as n →∞, Vn → 0 if N(n) ≤ (κ− 2)n, and Vn → 1 if N(n) ≥ (κ+ 2)n. A similar result holds for sampling u...
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