On the All-Farthest-Segments problem for a planar set of points
نویسندگان
چکیده
In this note, we outline a very simple algorithm for the following problem: Given a set S of n points p1, p2, p3, . . . , pn in the plane, we have O(n ) segments implicitly defined on pairs of these n points. For each point pi, find a segment from this set of implicitly defined segments that is farthest from pi. The complexity of our algorithm is in O(nh+n logn), where n is the number of input points, and h is the number of vertices on the convex hull of S.
منابع مشابه
An O(n log n) Algorithm for the All-Farthest-Segments Problem for a Planar Set of Points
In this paper, we propose an algorithm for computing the farthest-segment Voronoi diagram for the edges of a convex polygon and apply this to obtain an O(n logn) algorithm for the following proximity problem: Given a set P of n (>2) points in the plane, we have O(n2) implicitly defined segments on pairs of points. For each point p ∈ P , find a segment from this set of implicitly defined segment...
متن کاملOn co-Farthest Points in Normed Linear Spaces
In this paper, we consider the concepts co-farthest points innormed linear spaces. At first, we define farthest points, farthest orthogonalityin normed linear spaces. Then we define co-farthest points, co-remotal sets,co-uniquely sets and co-farthest maps. We shall prove some theorems aboutco-farthest points, co-remotal sets. We obtain a necessary and coecient conditions...
متن کاملSOME NEW RESULTS ON REMOTEST POINTS IN NORMED SPACES
In this paper, using the best proximity theorems for an extensionof Brosowski's theorem. We obtain other results on farthest points. Finally, wedene the concept of e- farthest points. We shall prove interesting relationshipbetween the -best approximation and the e-farthest points in normed linearspaces (X; ||.||). If z in W is a e-farthest point from an x in X, then z is also a-best approximati...
متن کامل(n,1,1,α)-Center Problem
Given a set of points in the plane and a constant ,-center problem is to find two closed disks which each covers the whole , the diameter of the bigger one is minimized, and the distance of the two centers is at least . Constrained -center problem is the -center problem in which the centers are forced to lie on a given line . In this paper, we first introduce -center problem and its constrain...
متن کاملOptimization of the Kinematic Sensitivity and the Greatest Continuous Circle in the Constant-orientation Workspace of Planar Parallel Mechanisms
This paper presents the results of a comprehensive study on the efficiency of planar parallel mechanisms, considering their kinetostatic performance and also, their workspace. This aim is approached upon proceeding single- and multi-objective optimization procedures. Kinetostatic performances of ten different planar parallel mechanisms are analyzed by resorting to a recent index, kinematic sens...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Inf. Process. Lett.
دوره 100 شماره
صفحات -
تاریخ انتشار 2006