منابع مشابه
Convex 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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The convex hull of X,,. . ., X., a sample of independent identically distributed Rd-valued random vectors with density f is called a random convex hull with parameters f and II. In this paper, we give an a orithm for the computer generation of random convex hulls when f is radial, i.e. when j(x) = g(ll $ l)Tor some function g. Then we look at the average time E(r) of the algorithm under a conve...
متن کاملConvex Hulls of Multidimensional Random Walks
Let Sk be a random walk in R such that its distribution of increments does not assign mass to hyperplanes. We study the probability pn that the convex hull conv(S1, . . . , Sn) of the first n steps of the walk does not include the origin. By providing an explicit formula, we show that for planar symmetrically distributed random walks, pn does not depend on the distribution of increments. This e...
متن کاملOn the Expected Complexity of Random Convex Hulls
In this paper we present several results on the expected complexity of a convex hull of n points chosen uniformly and independently from a convex shape. (i) We show that the expected number of vertices of the convex hull of n points, chosen uniformly and independently from a disk is O(n1/3), and O(k log n) for the case a convex polygon with k sides. Those results are well known (see [RS63, Ray7...
متن کاملSteaming 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 ...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1987
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-51-1-263-265