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On Exact Solutions to the Euclidean Bottleneck Steiner Tree Problem [chapter]

Sang Won Bae, Chunseok Lee, Sunghee Choi
2009 Lecture Notes in Computer Science  
of the longest edge in the tree is minimized.  ...  We study the Euclidean bottleneck Steiner tree problem: given a set P of n points in the Euclidean plane and a positive integer k, find a Steiner tree with at most k Steiner points such that the length  ...  Acknowledgement The authors thank anonymous referees for valuable comments to improve our paper.  ... 
doi:10.1007/978-3-642-00202-1_10 fatcat:4iphryw6cnho3cphr2n7l3jerq

On exact solutions to the Euclidean bottleneck Steiner tree problem

Sang Won Bae, Chunseok Lee, Sunghee Choi
2010 Information Processing Letters  
of the longest edge in the tree is minimized.  ...  We study the Euclidean bottleneck Steiner tree problem: given a set P of n points in the Euclidean plane and a positive integer k, find a Steiner tree with at most k Steiner points such that the length  ...  Acknowledgement The authors thank anonymous referees for valuable comments to improve our paper.  ... 
doi:10.1016/j.ipl.2010.05.014 fatcat:qycwg2tnczdclkffy3kmgcwche

Page 7258 of Mathematical Reviews Vol. , Issue 87m [page]

1987 Mathematical Reviews  
In Winter’s algorithm there are two stages in computing the exact Steiner minimal trees.  ...  COMPUTER SCIENCE 7258 Cockayne, E. J. (3-VCTR); Hewsgill, D. E. (3-VCTR) Exact computation of Steiner minimal trees in the plane. Inform. Process. Lett. 22 (1986), no. 3, 151-156.  ... 

Exact Algorithms for the Bottleneck Steiner Tree Problem [chapter]

Sang Won Bae, Sunghee Choi, Chunseok Lee, Shin-ichi Tanigawa
2009 Lecture Notes in Computer Science  
Given n terminals in the plane R 2 and a positive integer k, the bottleneck Steiner tree problem is to find k Steiner points in R 2 so that the longest edge length of the resulting Steiner tree is minimized  ...  Unlike the classical Steiner tree problem where the sum of the edge lengths of the Steiner tree is minimized, this problem asks a Steiner tree where the maximum of the edge lengths is minimized and the  ...  Given n points, called terminals, in the plane and a positive integer k, find a Steiner tree spanning all terminals and at most k Steiner points that minimizes the length of its longest edge. rectilinear  ... 
doi:10.1007/978-3-642-10631-6_5 fatcat:ovw2jxvx2bemxgxrm34rgjvpnq

A Dynamic Adaptive Relaxation Scheme Applied to the Euclidean Steiner Minimal Tree Problem

François Chapeau-Blondeau, Fabrice Janez, Jean-Louis Ferrier
1997 SIAM Journal on Optimization  
The Steiner problem is an NP-hard optimization problem which consists of finding the minimal-length tree connecting a set of N points in the Euclidean plane.  ...  Exact methods of resolution currently available are exponential in N , making exact minimal trees accessible for only small size problems (up to N ≈ 100).  ...  The solution of the Steiner problem is given by the Steiner tree of minimal length or minimal Steiner tree.  ... 
doi:10.1137/s1052623494275069 fatcat:drmssmsf7nfc7dqv6vr5niwqve

Page 6627 of Mathematical Reviews Vol. , Issue 92m [page]

1992 Mathematical Reviews  
A Steiner minimal tree of a set P of points in the plane is a shortest network spanning P.  ...  Let L,(P) and L,,(P) denote the lengths of the Steiner minimum tree and the minimum spanning tree, respectively, of a set P of n points in the plane.  ... 

Exact Algorithms for the Bottleneck Steiner Tree Problem

Sang Won Bae, Sunghee Choi, Chunseok Lee, Shin-ichi Tanigawa
2011 Algorithmica  
Given n terminals in the plane R 2 and a positive integer k, the bottleneck Steiner tree problem is to find k Steiner points in R 2 so that the longest edge length of the resulting Steiner tree is minimized  ...  Unlike the classical Steiner tree problem where the sum of the edge lengths of the Steiner tree is minimized, this problem asks a Steiner tree where the maximum of the edge lengths is minimized and the  ...  Given n points, called terminals, in the plane and a positive integer k, find a Steiner tree spanning all terminals and at most k Steiner points that minimizes the length of its longest edge. rectilinear  ... 
doi:10.1007/s00453-011-9553-y fatcat:spk7la3p45byriqnp7h2w3evaq

A 4-geometry maze router and its application on multiterminal nets

Gene Eu Jan, Ki-Yin Chang, Su Gao, Ian Parberry
2005 ACM Transactions on Design Automation of Electronic Systems  
Lee's algorithm and its variants, probably the most widely used maze routing method, fails to work in the 4-geometry of the grid plane.  ...  Next, to solve the obstacle-avoiding rectilinear and 4-geometry Steiner tree problems, a heuristic algorithm is presented.  ...  The problem of constructing Steiner minimal trees in the Euclidean plane without obstacles is NP-hard.  ... 
doi:10.1145/1044111.1044118 fatcat:g7eufvnaafc3tnlv7izg4i6jva

Page 4414 of Mathematical Reviews Vol. , Issue 2001G [page]

2001 Mathematical Reviews  
The first section of the book includes papers on the general geometric Steiner tree problem in the plane and higher dimensions.  ...  Warme, Winter and Zachariasen conclude the first part of the volume with a state-of- the art article on exact algorithms for the Euclidean and rectilinear Steiner problem in the plane.  ... 

Efficient Steiner Tree Construction Based on Spanning Graphs

H. Zhou
2004 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
Steiner Minimal Tree (SMT) problem is a very important problem in VLSI CAD.  ...  This paper records an implementation of an efficient Steiner minimal tree algorithm that has a worst case running time of O(n log n) and a similar performance as the Iterated 1-Steiner algorithm.  ...  Acknowledgments The author wants to thank Mr. Chuan Lin for help running the experiments.  ... 
doi:10.1109/tcad.2004.826557 fatcat:ge2tzjbxxfb4jn2yl4wuckqj7i

Spanning graph-based nonrectilinear steiner tree algorithms

Qi Zhu, Hai Zhou, Tong Jing, X.-L. Hong, Yang Yang
2005 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
In an interconnect architecture, the Steiner minimal tree (SMT) construction is one of the key problems.  ...  In this paper, we give two practical octilinear Steiner minimal tree (OSMT) construction algorithms based on octilinear spanning graphs (OSGs).  ...  As the foundation of octilinear interconnect, an octilinear Steiner minimal tree (OSMT) connects given points in the octilinear plane, which allows 45 diagonal interconnections in addition to traditional  ... 
doi:10.1109/tcad.2005.850862 fatcat:e5movnqpvzbtfisb4sqwtsqa6a

Efficient Steiner tree construction based on spanning graphs

Hai Zhou
2003 Proceedings of the 2003 international symposium on Physical design - ISPD '03  
Steiner Minimal Tree (SMT) problem is a very important problem in VLSI CAD.  ...  This paper records an implementation of an efficient Steiner minimal tree algorithm that has a worst case running time of O(n log n) and a similar performance as the Iterated 1-Steiner algorithm.  ...  Acknowledgments The author wants to thank Mr. Chuan Lin for help running the experiments.  ... 
doi:10.1145/640000.640034 dblp:conf/ispd/Zhou03 fatcat:ega7ildq6jc5hoblhgpnoddaqe

Efficient Steiner tree construction based on spanning graphs

Hai Zhou
2003 Proceedings of the 2003 international symposium on Physical design - ISPD '03  
Steiner Minimal Tree (SMT) problem is a very important problem in VLSI CAD.  ...  This paper records an implementation of an efficient Steiner minimal tree algorithm that has a worst case running time of O(n log n) and a similar performance as the Iterated 1-Steiner algorithm.  ...  Acknowledgments The author wants to thank Mr. Chuan Lin for help running the experiments.  ... 
doi:10.1145/640033.640034 fatcat:ivhorz7paracjechsu4a755dbe

Determining Sensor Locations in Wireless Sensor Networks

Zimao Li, Wenying Xiao
2015 International Journal of Distributed Sensor Networks  
The problem is in fact the bottleneck Steiner tree problem, trying to find a Steiner tree minimizing the length of the longest edges for the given n terminals in the Euclidean plane by introducing at most  ...  A restricted bottleneck Steiner tree problem is studied in this paper, which requires that only degree ≥3 Steiner points are not allowed to be adjacent in the optimal solution.  ...  Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper.  ... 
doi:10.1155/2015/914625 fatcat:c3a2x7ksqfbkdns7sjmofcm4zy

Weighted Euclidean Steiner Trees for Disaster-Aware Network Design

Luis Garrote, Lucia Martins, Urbano J. Nunes, Martin Zachariasen
2019 2019 15th International Conference on the Design of Reliable Communication Networks (DRCN)  
We consider the problem of constructing a Euclidean Steiner tree in a setting where the plane has been divided into polygonal regions, each with an associated weight.  ...  The problem is a natural generalization of the obstacle-avoiding Euclidean Steiner tree problem, and has obvious applications in network design.  ...  article is based upon work from COST Action CA1512 ("Resilient communication services protecting end-user applications from disaster based failures -RECODIS") supported by COST (European Cooperation in  ... 
doi:10.1109/drcn.2019.8713664 dblp:conf/drcn/GarroteMNZ19 fatcat:gzgpyc6mcnav5fhj4bhwfv7tga
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