منابع مشابه
Computing Farthest Neighbors on a Convex Polytope
Let be a set of points in convex position in . The farthest-point Voronoi diagram of partitions into convex cells. We consider the intersection of the diagram with the boundary of the convex hull of . We give an algorithm that computes an implicit representation of in expected time. More precisely, we compute the combinatorial structure of , the coordinates of its vertices, and the equation of ...
متن کاملGibbs/Metropolis algorithms on a convex polytope
This paper gives sharp rates of convergence for natural versions of the Metropolis algorithm for sampling from the uniform distribution on a convex polytope. The singular proposal distribution, based on a walk moving locally in one of a fixed, finite set of directions, needs some new tools. We get useful bounds on the spectrum and eigenfunctions using Nash and Weyltype inequalities. The top eig...
متن کاملThe Intersection of Convex Transversals is a Convex Polytope
It is proven that the intersection of convex transversals of finitely many sets in R is a convex polytope, possibly empty. Related results on support hyperplanes and complements of finite unions of convex sets are given. MSC 2000: 52A20
متن کاملThe Mean Width of a Convex Polytope
In the case n=d = 2, because of Cauchy's surface-area formula [2; p. 208], relation (3) reduces to the trivial statement that the perimeter of a convex polygon is equal to the sum of the lengths of its edges. If K is any closed bounded convex set of dimension at most d, we may write KaEczE and use md(K) and mn(K) to denote the mean widths of K relative to the spaces E and E respectively. A simp...
متن کاملOn Convex Subsets in Tournaments
A tournament is a complete directed graph. A convex subset is a vertex subset with the property that every two-path beginning and ending inside the convex subset is contained completely within the subset. This paper shows that every nontrivial convex subset is the closure of a subset of vertices of cardinality two. This result leads to algorithms that nd all convex subsets in a tournament in O(...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1972
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1972-0301633-6