Geometry of minimal networks and the one-dimensional Plateau problem
Geometry of minimal networks and the one-dimensional Plateau problem
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最小网络的几何和一维 Plateau 问题
DOI：
10.1070/rm1992v047n02abeh000878
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发表时间：
1992
期刊：
影响因子：
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通讯作者：
A. Tuzhilin
中科院分区：
文献类型：
--
作者：
A. Ivanov;A. Tuzhilin
第1节. Steiner问题及其变式1.1.基本定义全局最小网络1.3.局部最小网络1.4.封闭网络和具有固定边界的网络1.5.最小网络的局部结构1.6.经典环境空间中的最小网络1.6.1.二维欧几里得平面的情况1.6.2.二维闭曲面的情况1.6.3.多面体的情况1.6.4.三维欧氏空间的情况§2。平面上的全局极小网络2.1.最小生成树旅行推销员问题2.3.最小Steiner树2.3.1. Lune属性2.3.2.楔形特性2.3.3.双楔特性2.3.4.最小Steiner树和EMST之间的连接2.3.5.钻石属性2.3.6.凸船体和Steiner船体2.3.7.最小Steiner树和Simpson线2.4.斯坦纳比率2.5。全局最小网络跨越点躺在“阶梯”和“之字形线“2.6.全局最小网络的点位于一个圆圈2.7。寻找最小Steiner树的改进算法§3.平面上的局部极小网络3.1.具有凸边界的极小2-树的完全分类3.1.1.轮换次数3.1.2.旋转数不超过5的2-树的镶木地板实现3.1.3. Parquets及其属性3.1.4.分类定理3.2.具有凸边界的非退化极小网络。循环情况3.2.1.平凡网络及其旋转数3.2.2.网络的Parquet实现与凸极小实现3.2.3.用凸最小实现描述网络的parquets 3.3.正则n边形顶点的极小2-树3.4。退化Steiner树的凸极小实现参考文献
CONTENTSIntroduction §1. The Steiner problem and its variations1.1. Fundamental definitions1.2. Globally minimal networks1.3. Locally minimal networks1.4. Closed networks and networks with a fixed boundary1.5. Local structure of minimal networks1.6. Minimal networks in classical ambient spaces1.6.1. The case of the two-dimensional Euclidean plane1.6.2. The case of two-dimensional closed surfaces1.6.3. The case of polyhedra1.6.4. The case of three-dimensional Euclidean space §2. Globally minimal networks on the plane2.1. Minimal spanning trees2.2. Travelling salesperson problem2.3. Minimal Steiner trees2.3.1. Lune property2.3.2. Wedge property2.3.3. Double wedge property2.3.4. Connection between the minimal Steiner tree and the EMST2.3.5. Diamond property2.3.6. Convex hull and Steiner hull2.3.7. The minimal Steiner tree and the Simpson lines2.4. Steiner ratio2.5. Globally minimal networks spanning points lying on a "ladder" and a "zigzag line"2.6. Globally minimal networks spanning points lying on a circle2.7. Improved algorithm for finding a minimal Steiner tree §3. Locally minimal networks on the plane3.1. Complete classification of minimal 2-trees with a convex boundary3.1.1. Rotation number3.1.2. Parquet realization of 2-trees with rotation number not exceeding five3.1.3. Parquets and their properties3.1.4. Classification theorems3.2. Non-degenerate minimal networks with a convex boundary. Cyclic case3.2.1. Trivial networks and their rotation numbers3.2.2. Parquet realization of networks with a convex minimal realization3.2.3. Description of parquets of networks with a convex minimal realization3.3. Minimal 2-trees spanning the vertices of regular n-gons3.4. Convex minimal realization of degenerate Steiner treesReferences
影响因子：
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作者：
PRIM, RC
通讯作者：
PRIM, RC