منابع مشابه
Formalizing 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...
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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 ...
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For xed integers k 3 and hypergraphs G on N vertices, which contain edges of cardinalities at most k, and are uncrowded, i.e., do not contain cycles of lengths 2; 3, or 4, and with average degree for the i-element edges bounded by O(T i 1 (lnT )(k i)=(k 1)), i = 3; : : : ; k, for some number T 1, we show that the independence number (G) satis es (G) = ((N=T ) (lnT )1=(k 1)). Moreover, an indepe...
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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...
متن کاملConvex Hulls for Random Lines
Consider n i .i .d . random lines in the plane defined by their slope and distance from the origin . The slope is uniformly distributed on (0, 27r] and independent of the distance R from the origin . These lines define a set I of n(n 1)/2 intersection points . It was recently shown by Atallah and Ching and Lee that the cardinality of the convex hull of these intersection points is 0(n), and the...
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ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
سال: 2003
ISSN: 0294-1449
DOI: 10.1016/s0294-1449(02)00007-0