Algorithms for bivariate medians and a Fermat-Torricelli problem for lines

被引：17

作者：

Aloupis, G

Langerman, S

Soss, M

Toussaint, G

机构：

[1] McGill Univ, Sch Comp Sci, Montreal, PQ H3A 2A7, Canada

[2] Chem Comp Grp, Montreal, PQ H3A 2R7, Canada

来源：

COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS | 2003年 / 26卷 / 01期

关键词：

Oja depth; simplicial depth; Fermat-Torricelli problem; geometric medians; estimators of location; algorithms; computational geometry;

D O I：

10.1016/S0925-7721(02)00173-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a set S of n points in R-2, the Oja depth of a point theta is the sum of the areas of all triangles formed by theta and two elements of S. A point in R-2 with minimum depth is an Oja median. We show how an Oja median may be computed in O(n log(3) n) time. In addition, we present an algorithm for computing the Fermat-Torricelli points of n lines in O(n) time. These points minimize the sum of weighted distances to the lines. Finally, we propose an algorithm which computes the simplicial median of S in O(n(4)) time. This median is a point in R-2 which is contained in the most triangles formed by elements of S. (C) 2003 Elsevier Science B.V. All rights reserved.

引用

页码：69 / 79

页数：11

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