منابع مشابه
Covering Random Points in a Unit Disk
Let D be the punctured unit disk. It is easy to see that no pair x, y in D can cover D in the sense that D cannot be contained in the union of the unit disks centred at x and y. With this fact in mind, let Vn = {X1, X2, . . . , Xn}, where X1, X2, . . . are random points sampled independently from a uniform distribution on D. We prove that, with asymptotic probability one, there are two points i...
متن کاملCovering Random Points in a Unit Ball
Choose random pointsX1, X2, X3, . . . independently from a uniform distribution in a unit ball in <. Call Xn a dominator iff distance(Xn, Xi) ≤ 1 for all i < n, i.e. the first n points are all contained in the unit ball that is centered at the n’th point Xn. We prove that, with probability one, only finitely many of the points are dominators. For the special casem = 2, we consider the unit disk...
متن کاملOn random points in the unit disk
Let n be a positive integer and λ > 0 a real number. Let Vn be a set of n points in the unit disk selected uniformly and independently at random. Define G(λ, n) to be the graph with vertex set Vn, in which two vertices are adjacent if and only if their Euclidean distance is at most λ. We call this graph a unit disk random graph. Let λ = c √ lnn/n and let X be the number of isolated points in G(...
متن کاملCovering Points by Isothetic Unit Squares
Given a set P of n points in R, we consider two related problems. Firstly, we study the problem of computing two isothetic unit squares which may be either disjoint or intersecting (having empty common zone) such that they together cover maximum number of points. The time and space complexities of the proposed algorithm for this problem are both O(n). We also study the problem of computing k di...
متن کاملCovering Points with Disjoint Unit Disks
We consider the following problem. How many points must be placed in the plane so that no collection of disjoint unit disks can cover them? The answer, k, is already known to satisfy 11 ≤ k ≤ 53. Here, we improve the lower bound to 13 and the upper bound to 50. We also provide a set of 45 points that apparently cannot be covered, although this has been determined via computer search.
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ژورنال
عنوان ژورنال: Advances in Applied Probability
سال: 2008
ISSN: 0001-8678,1475-6064
DOI: 10.1239/aap/1208358884