Absorbing Angles, Steiner Minimal Trees, and Antipodality

被引：0
|
作者：
H. Martini
K. J. Swanepoel
P. Oloff de Wet
机构：
[1] Technische Universität Chemnitz,Fakultät für Mathematik
[2] University of South Africa,Department of Decision Sciences
来源：
Journal of Optimization Theory and Applications | 2009年 / 143卷
关键词：
Steiner minimal trees; Absorbing angles; Antipodality; Face antipodality; Minkowski geometry;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We give a new proof that a star {opi:i=1,…,k} in a normed plane is a Steiner minimal tree of vertices {o,p1,…,pk} if and only if all angles formed by the edges at o are absorbing (Swanepoel in Networks 36: 104–113, 2000). The proof is simpler and yet more conceptual than the original one.
引用
收藏
页码：149 / 157
页数：8
相关论文
共 50 条
  • [41] Using a Conic Formulation for Finding Steiner Minimal Trees
    Marcia Fampa
    Nelson Maculan
    Numerical Algorithms, 2004, 35 : 315 - 330
  • [42] IDENTIFYING STEINER MINIMAL TREES ON FOUR POINTS IN SPACE
    Weng, J. F.
    Thomas, D. A.
    Mareels, I.
    DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2009, 1 (03) : 401 - 411
  • [43] STEINER MINIMAL-TREES ON SETS OF 4 POINTS
    DU, DZ
    HWANG, FK
    SONG, GD
    TING, GY
    DISCRETE & COMPUTATIONAL GEOMETRY, 1987, 2 (04) : 401 - 414
  • [44] A DECOMPOSITION THEOREM ON EUCLIDEAN STEINER MINIMAL-TREES
    HWANG, FK
    SONG, GD
    TING, GY
    DU, DZ
    DISCRETE & COMPUTATIONAL GEOMETRY, 1988, 3 (04) : 367 - 382
  • [45] STEINER MINIMAL-TREES AND URBAN SERVICE NETWORKS
    SMITH, JM
    GROSS, M
    SOCIO-ECONOMIC PLANNING SCIENCES, 1982, 16 (01) : 21 - 38
  • [46] k-Steiner-minimal-trees in metric spaces
    Cieslik, D
    DISCRETE MATHEMATICS, 1999, 208 : 119 - 124
  • [47] IMPROVED COMPUTATION OF PLANE STEINER MINIMAL-TREES
    COCKAYNE, EJ
    HEWGILL, DE
    ALGORITHMICA, 1992, 7 (2-3) : 219 - 229
  • [48] A NEW BOUND FOR EUCLIDEAN STEINER MINIMAL-TREES
    CHUNG, FRK
    GRAHAM, RL
    ANNALS OF THE NEW YORK ACADEMY OF SCIENCES, 1985, 440 : 328 - 346
  • [49] Using a conic formulation for finding Steiner minimal trees
    Fampa, M
    Maculan, N
    NUMERICAL ALGORITHMS, 2004, 35 (2-4) : 315 - 330
  • [50] Minimal Steiner trees for rectangular arrays of lattice points
    Brazil, M
    Rubinstein, JH
    Thomas, DA
    Weng, JF
    Wormald, NC
    JOURNAL OF COMBINATORIAL THEORY SERIES A, 1997, 79 (02) : 181 - 208
12345