نتایج جستجو برای: co farthest points

تعداد نتایج: 591428  

2005
Boaz Ben-Moshe Binay K. Bhattacharya Qiaosheng Shi

We propose an implicit representation for the farthest Voronoi Diagram of a set P of n points in the plane lying outside a set R of m disjoint axes-parallel rectangular obstacles. The distances are measured according to the L1 shortest path (geodesic) metric. In particular, we design a data structure of size O(N) in O(N log N) time that supports O(N logN)-time farthest point queries (where N = ...

Journal: :SIAM J. Comput. 1982
Andrew Chi-Chih Yao

The problem of finding a minimum spaYlning tree connecting n points in a k-dimensional space is discussed under three comon distance metrics -Euclidean, rectilinear, and L . co By employing a subroutine that -=. solves the post office problem, we show that, for fixed k 2 3 , such a minimum spanning tree can be found in time O(n2’&Ck)(log n)l-a(k)) 9 where a(k) = 2 -(k+l) 1.8 . The bound can be ...

Journal: :Discrete Applied Mathematics 2015
Tristan Roussillon

A digital edge is a digitization of a straight segment joining two points of integer coordinates. Such a digital set may be analytically defined by the rational slope of the straight segment. We show in this paper that the convex hull, the Euclidean farthest-point Voronoi diagram as well as the dual farthest-point Delaunay triangulation of a digital edge can be fully described by the continued ...

Journal: :Journal of Approximation Theory 2010
Rafael Espínola Chong Li Genaro López-Acedo

Let A be a nonempty closed subset (resp. nonempty bounded closed subset) of a metric space (X, d) and x ∈ X \ A. The nearest point problem (resp. the farthest point problem) w.r.t. x considered here is to find a point a0 ∈ A such that d(x, a0) = inf{d(x, a) : a ∈ A} (resp. d(x, a0) = sup{d(x, a) : a ∈ A}). We study the well posedness of nearest point problems and farthest point problems in geod...

Journal: :Adv. in Math. of Comm. 2016
Daniele Bartoli Alexander A. Davydov Massimo Giulietti Stefano Marcugini Fernanda Pambianco

Multiple coverings of the farthest-off points ((R,μ)-MCF codes) and the corresponding (ρ, μ)-saturating sets in projective spaces PG(N, q) are considered. We propose some methods which allow us to obtain new small (1, μ)-saturating sets and short (2, μ)-MCF codes with μ-density either equal to 1 (optimal saturating sets and almost perfect MCF-codes) or close to 1 (roughly 1+1/cq, c ≥ 1). In par...

Journal: :Int. J. Math. Mathematical Sciences 2011
Sharifa Naem Al-Sharif M. Rawashdeh

Let X be a Banach space and let G be a closed bounded subset of X. For x1, x2, . . . , xm ∈ X, we set ρ x1, x2, . . . , xm,G sup{max1≤i≤m‖xi−y‖ : y ∈ G}. The setG is called simultaneously remotal if, for any x1, x2, . . . , xm ∈ X, there exists g ∈ G such that ρ x1, x2, . . . , xm,G max1≤i≤m‖xi−g‖. In this paper, we show that if G is separable simultaneously remotal in X, then the set of ∞Bochn...

Journal: :Electronic Notes in Discrete Mathematics 2013
Fernanda Pambianco Alexander A. Davydov Daniele Bartoli Massimo Giulietti Stefano Marcugini

In this work we summarize some recent results, to be included in a forthcoming paper [1]. We define μ-density as a characteristic of quality for the kind of coverings codes called multiple coverings of the farthest-off points (MCF). A concept of multiple saturating sets ((ρ, μ)-saturating sets) in projective spaces PG(N, q) is introduced. A fundamental relationship of these sets with MCF is sho...

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