Intersecting Convex Sets by Rays

被引：0
|
作者：
Radoslav Fulek
Andreas F. Holmsen
János Pach
机构：
[1] Simon Fraser University,School of Computing Science
[2] KAIST,Division of Computer Science
[3] City College of New York,Department of Computer Science
来源：
Discrete & Computational Geometry | 2009年 / 42卷
关键词：
Convex sets; Geometric transversals; Depth in hyperplane arrangements; Regression depth;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
What is the smallest number τ=τ(n) such that for any collection of n pairwise disjoint convex sets in d-dimensional Euclidean space, there is a point such that any ray (half-line) emanating from it meets at most τ sets of the collection? This question of Urrutia is closely related to the notion of regression depth introduced by Rousseeuw and Hubert (1996). We show the following:
引用
收藏
页码：343 / 358
页数：15
相关论文
共 50 条
  • [41] Intersecting two families of sets on the GPU
    Fort, Marta
    Antoni Sellares, J.
    Valladares, Nacho
    JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING, 2017, 104 : 167 - 178
  • [42] Finding Convex Sets in Convex Position
    Géza Tóth
    Combinatorica, 2000, 20 : 589 - 596
  • [43] Finding convex sets in convex position
    Tóth, G
    COMBINATORICA, 2000, 20 (04) : 589 - 596
  • [44] A NEW LINEAR ALGORITHM FOR INTERSECTING CONVEX POLYGONS
    OROURKE, J
    CHIEN, CB
    OLSON, T
    NADDOR, D
    COMPUTER GRAPHICS AND IMAGE PROCESSING, 1982, 19 (04): : 384 - 391
  • [45] Discrete Q-Convex Sets Reconstruction from Discrete Point X-Rays
    Abdmouleh, Fatma
    Daurat, Alain
    Tajine, Mohamed
    COMBINATORIAL IMAGE ANALYSIS, 2011, 6636 : 321 - 334
  • [46] Voronoi Diagram for Intersecting Convex Polygons in the Plane
    Lu J.
    Xiong P.
    Min W.
    Liao Y.
    Jisuanji Fuzhu Sheji Yu Tuxingxue Xuebao/Journal of Computer-Aided Design and Computer Graphics, 2019, 31 (09): : 1609 - 1616
  • [47] INTERSECTING ALL EDGES OF CONVEX POLYTOPES BY PLANES
    KATCHALSKI, M
    DISCRETE MATHEMATICS, 1977, 19 (03) : 273 - 279
  • [48] A simple linear algorithm for intersecting convex polygons
    Toussaint, Godfried T.
    VISUAL COMPUTER, 1985, 1 (02): : 118 - 123
  • [49] Tverberg-Type Theorems for Intersecting by Rays
    R. N. Karasev
    Discrete & Computational Geometry, 2011, 45 : 340 - 347
  • [50] Tverberg-Type Theorems for Intersecting by Rays
    Karasev, R. N.
    DISCRETE & COMPUTATIONAL GEOMETRY, 2011, 45 (02) : 340 - 347
12345