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

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. ...

##
###
On exact solutions to the Euclidean bottleneck Steiner tree problem

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. ...

##
###
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]

2009
*
Lecture Notes in Computer Science
*

Given n terminals

doi:10.1007/978-3-642-10631-6_5
fatcat:ovw2jxvx2bemxgxrm34rgjvpnq
*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 ...##
###
A Dynamic Adaptive Relaxation Scheme Applied to the Euclidean Steiner Minimal Tree Problem

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*. ...

##
###
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

2011
*
Algorithmica
*

Given n terminals

doi:10.1007/s00453-011-9553-y
fatcat:spk7la3p45byriqnp7h2w3evaq
*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 ...##
###
A 4-geometry maze router and its application on multiterminal nets

2005
*
ACM Transactions on Design Automation of Electronic Systems
*

Lee's algorithm and its variants, probably

doi:10.1145/1044111.1044118
fatcat:g7eufvnaafc3tnlv7izg4i6jva
*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. ...##
###
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

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. ...

##
###
Spanning graph-based nonrectilinear steiner tree algorithms

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 ...

##
###
Efficient Steiner tree construction based on spanning graphs

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. ...

##
###
Efficient Steiner tree construction based on spanning graphs

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. ...

##
###
Determining Sensor Locations in Wireless Sensor Networks

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. ...

##
###
Weighted Euclidean Steiner Trees for Disaster-Aware Network Design

2019
*
2019 15th International Conference on the Design of Reliable Communication Networks (DRCN)
*

We consider

doi:10.1109/drcn.2019.8713664
dblp:conf/drcn/GarroteMNZ19
fatcat:gzgpyc6mcnav5fhj4bhwfv7tga
*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*...
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