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
  • [1] Intersecting Convex Sets by Rays
    Fulek, Radoslav
    Holmsen, Andreas F.
    Pach, Janos
    DISCRETE & COMPUTATIONAL GEOMETRY, 2009, 42 (03) : 343 - 358
  • [2] Intersecting Convex Sets by Rays
    Fulek, Radoslav
    Holmsen, Andreas F.
    Pach, Janos
    PROCEEDINGS OF THE TWENTY-FOURTH ANNUAL SYMPOSIUM ON COMPUTATIONAL GEOMETRY (SGG'08), 2008, : 385 - 391
  • [3] Piercing intersecting convex sets
    Barany, Imre
    Dillon, Travis
    Palvolgyi, Domotor
    Varga, Daniel
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2025, 710 : 405 - 417
  • [4] INTERSECTING UNIONS OF MAXIMAL CONVEX SETS
    BREEN, M
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 39 (03) : 587 - 590
  • [5] Transversals to Colorful Intersecting Convex Sets
    Gomez-Navarro, Cuauhtemoc
    Roldan-Pensado, Edgardo
    DISCRETE & COMPUTATIONAL GEOMETRY, 2024,
  • [6] INTERSECTING UNIONS OF CONVEX-SETS IN RN
    BREEN, M
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 51 (02) : 427 - 431
  • [7] SETS OF NON-SELF-INTERSECTING PATHS CONNECTING THE VERTICES OF A CONVEX POLYGON
    Kortezov, Ivaylo
    MATHEMATICS AND INFORMATICS, 2022, 65 (06): : 546 - 555
  • [8] Determination of Q-convex sets by X-rays
    Daurat, A
    THEORETICAL COMPUTER SCIENCE, 2005, 332 (1-3) : 19 - 45
  • [9] Convex-along-rays functions and star-shaped sets
    Rubinov, A
    Vladimirov, A
    NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 1998, 19 (5-6) : 593 - 613
  • [10] Reconstruction of Convex Sets from One or Two X-rays
    Gerard, Yan
    FUNDAMENTA INFORMATICAE, 2022, 189 (02) : 113 - 143
12345