Polynomial ranges are commonly used for numerically solving polynomial systems with interval Newton solvers. Often ranges are computed using the convex hull property of the tensor...
We give a new class of outer bounds on the marginal polytope, and propose a cutting-plane algorithm for efficiently optimizing over these constraints. When combined with a concav...
Color red and blue the n vertices of a convex polytope P in R3 . Can we compute the convex hull of each color class in o(n log n)? What if we have χ > 2 colors? What if the co...
Let P be a random 0/1-polytope in d with n(d) vertices, and denote by k(P) the k-face density of P, i.e., the quotient of the number of k-dimensional faces of P and `n(d) k+1
We show that half-integral polytopes obtained as the convex hull of a random set of half-integral points of the 0/1 cube have rank as high as Ω(log n/ log log n) with positive pr...