منابع مشابه
Steaming on Convex Hulls
This is a sea story about using a simple classroom example to save a great deal of money, as well as to convince beginning Postgraduate Naval School operations research students—experienced, skeptical military officers—that mathematical analysis can yield immediate results. The application is planning a ship’s transit from one point to another in a fixed amount of time, given that the ship can ...
متن کاملOn the visibility graph of convex translates
We show that the visibility graph of a set of non-intersecting translates of the same compact convex object in R always contains a Hamiltonian path. Furthermore, we show that every other edge in the Hamiltonian path can be used to obtain a perfect matching that is realized by a set of non-intersecting lines of sight. ? 2001 Elsevier Science B.V. All rights reserved.
متن کاملOn the Smoothed Complexity of Convex Hulls
We establish an upper bound on the smoothed complexity of convex hulls in R under uniform Euclidean (`2) noise. Specifically, let {p1, p2, . . . , pn} be an arbitrary set of n points in the unit ball in R and let pi = pi + xi, where x1, x2, . . . , xn are chosen independently from the unit ball of radius δ. We show that the expected complexity, measured as the number of faces of all dimensions,...
متن کاملFormalizing Convex Hulls Algorithms
We study the development of formally proved algorithms for computational geometry. The result of this work is a formal description of the basic principles that make convex hull algorithms work and two programs that implement convex hull computation and have been automatically obtained from formally verified mathematical proofs. A special attention has been given to handling degenerated cases th...
متن کاملConvex hulls of spheres and convex hulls of disjoint convex polytopes
Given a set Σ of spheres in E, with d ≥ 3 and d odd, having a constant number of m distinct radii ρ1, ρ2, . . . , ρm, we show that the worst-case combinatorial complexity of the convex hull of Σ is Θ( ∑ 1≤i6=j≤m nin ⌊ d 2 ⌋ j ), where ni is the number of spheres in Σ with radius ρi. To prove the lower bound, we construct a set of Θ(n1+n2) spheres in E , with d ≥ 3 odd, where ni spheres have rad...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1963
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1963.13.97