Minimum rectilinear Steiner tree of n points in the unit square

被引：1

作者：

Dumitrescu, Adrian ^{[1
]}

Jiang, Minghui ^{[2
]}

机构：

[1] Univ Wisconsin, Dept Comp Sci, Milwaukee, WI 53201 USA

[2] Utah State Univ, Dept Comp Sci, Logan, UT 84322 USA

来源：

COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS | 2018年 / 68卷

关键词：

Minimum rectilinear Steiner tree; Integer partition; Packing; Covering; HEURISTIC ALGORITHMS; DISTANCE;

D O I：

10.1016/j.comgeo.2017.06.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Chung and Graham conjectured (in 1981) that n points in the unit square [0,1](2) can be connected by a rectilinear Steiner tree of length at most root n + 1. Here we confirm this conjecture for small values of n, and for some new infinite sequences of values of n (but not for all n). As an interesting byproduct we obtain close rational approximations of root n from below, for those n. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：253 / 261

页数：9

共 50 条

[1] Algorithm for the construction of Rectilinear Steiner Minimum Tree by identifying the clusters of points
Vani, V.
Prasad, G. R.
2014 INTERNATIONAL CONFERENCE ON INFORMATION COMMUNICATION AND EMBEDDED SYSTEMS (ICICES), 2014,
[2] On the Minimum Spanning Tree Determined by n Points in the Unit Square
叶继昌
徐寅峰
徐成贤
Chinese Quarterly Journal of Mathematics, 1999, (02) : 76 - 82
[3] A practical algorithm for the minimum rectilinear steiner tree
Jun Ma
Bo Yang
Shaohan Ma
Journal of Computer Science and Technology, 2000, 15 : 96 - 99
[4] A practical algorithm for the minimum rectilinear Steiner tree
Ma, J
Yang, B
Ma, SH
JOURNAL OF COMPUTER SCIENCE AND TECHNOLOGY, 2000, 15 (01) : 96 - 99
[5] COMPUTING A RECTILINEAR STEINER MINIMAL TREE IN NO(SQUARE-ROOT-N) TIME
THOMBORSON, CD
DENEEN, LL
SHUTE, GM
LECTURE NOTES IN COMPUTER SCIENCE, 1987, 269 : 176 - 183
[6] The Euclidean bottleneck Steiner tree and Steiner tree with minimum number of Steiner points
Du, DZ
Wang, LS
Xu, BA
COMPUTING AND COMBINATORICS, 2001, 2108 : 509 - 518
[7] CONSTRUCTING THE OPTIMAL RECTILINEAR STEINER TREE DERIVABLE FROM A MINIMUM SPANNING TREE
HO, JM
VIJAYAN, G
WONG, CK
1989 IEEE INTERNATIONAL CONFERENCE ON COMPUTER-AIDED DESIGN: DIGEST OF TECHNICAL PAPERS, 1989, : 6 - 9
[8] REST: Constructing Rectilinear Steiner Minimum Tree via Reinforcement Learning
Liu, Jinwei
Chen, Gengjie
Young, Evangeline F. Y.
2021 58TH ACM/IEEE DESIGN AUTOMATION CONFERENCE (DAC), 2021, : 1135 - 1140
[9] Obstacle Aware Delay Optimized Rectilinear Steiner Minimum Tree Routing
Shyamala, G.
Prasad, G. R.
2017 2ND IEEE INTERNATIONAL CONFERENCE ON RECENT TRENDS IN ELECTRONICS, INFORMATION & COMMUNICATION TECHNOLOGY (RTEICT), 2017, : 2194 - 2197
[10] HEURISTICS FOR THE MINIMUM RECTILINEAR STEINER TREE PROBLEM - NEW ALGORITHMS AND A COMPUTATIONAL STUDY
DESOUZA, CC
RIBEIRO, CC
DISCRETE APPLIED MATHEMATICS, 1993, 45 (03) : 205 - 220

← 1 2 3 4 5 →