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Short trees in polygons

Pawel Winter, Martin Zachariasen, Jens Nielsen
2002 Discrete Applied Mathematics  
Next, these algorithms are used in a fast polynomial heuristic based on the concatenation of trees for appropriately selected subsets with up to four terminals.  ...  We consider the problem of determining a short Euclidean tree spanning a number of terminals in a simple polygon.  ...  When concatenated in greedy fashion (avoiding cycles), a reasonable solution to the Euclidean Steiner tree problem for any number of terminals inside a polygon is obtained.  ... 
doi:10.1016/s0166-218x(01)00256-6 fatcat:e5bun72jlfacnjqxvcmynshzl4

The GeoSteiner software package for computing Steiner trees in the plane: an updated computational study

Daniel Juhl, David M. Warme, Pawel Winter, Martin Zachariasen
2018 Mathematical Programming Computation  
The GeoSteiner software package has for more than 10 years been the fastest (publicly available) program for computing exact solutions to Steiner tree problems in the plane.  ...  The computational study by Warme, Winter and Zachariasen, published in 2000, documented the performance of the GeoSteiner approach -allowing the exact solution of Steiner tree problems with more than a  ...  New Greedy Euclidean Steiner Tree Heuristic The Zachariasen-Winter greedy heuristic for Euclidean Steiner trees [29] was added as an alternative to the existing Smith-Lee-Liebman heuristic [22] .  ... 
doi:10.1007/s12532-018-0135-8 fatcat:bxhgnp2minekzhtsfburlpdnvi

Obstacle-Avoiding Euclidean Steiner Trees in the Plane: An Exact Algorithm [chapter]

Martin Zachariasen, Pawel Winter
1999 Lecture Notes in Computer Science  
The rst exact algorithm for the obstacle-avoiding Euclidean Steiner tree problem in the plane (in its most general form) is presented.  ...  The algorithm uses a two-phase framework | based on the generation and concatenation of full Steiner trees | previously shown to be very successful for the obstacle-free case.  ...  The authors would like to thank David M. Warme for valuable discussions concerning the integer programming formulation and implementation.  ... 
doi:10.1007/3-540-48518-x_17 fatcat:u5xtjxt7ofhdljkbbrz34qyyue

Page 5114 of Mathematical Reviews Vol. , Issue 2000g [page]

2000 Mathematical Reviews  
[Winter, Pawel] (DK-CPNH-C; Copenhagen) Concatenation-based greedy heuristics for the Euclidean Steiner tree problem. (English summary) Algorithmica 25 (1999), no. 4, 418-437.  ...  Summary: “We present a class of O(mlogn) heuristics for the Steiner tree problem in the Euclidean plane.  ... 

Euclidean Steiner minimal trees with obstacles and Steiner visibility graphs

Pawel Winter
1993 Discrete Applied Mathematics  
Their applicability in connection with the construction of good quality suboptimal solutions to the Euclidean Steiner tree problem with obstacles is discussed.  ...  The notion of Steiner visibility graphs is introduced.  ...  Beasley [3] suggested a heuristic for the Euclidean Steiner tree problem that considers all connected subtrees of the minimum spanning tree for Z with four terminals.  ... 
doi:10.1016/0166-218x(93)90092-3 fatcat:qtuj22mptfcg7cdqezudgnrfc4

A Sausage Heuristic for Steiner Minimal Trees in Three-Dimensional Euclidean Space

Badri Toppur, J. MacGregor Smith
2005 Journal of Mathematical Modelling and Algorithms  
The classical algorithm for solving the Steiner Minimal Tree problem in the plane is by Melzak [11] .  ...  When one uses the Euclidean metric to compute these inter-connections, this is referred to as the Euclidean Steiner Minimal Tree Problem. This is an NP-hard problem.  ...  Acknowledgements The authors wish to acknowledge the care taken by the referees and the editor, who offered detailed criticism to improve the correctness and presentation of material in the paper.  ... 
doi:10.1007/s10852-004-6390-x fatcat:t2bcviu5bzbsfedui5t7r4dxha

A Parallel Steiner Tree Construction on the Server-Client Model of Computation

Rashid Bin Muhammad
2008 Fifth International Conference on Information Technology: New Generations (itng 2008)  
This paper presents the computational analysis of the Steiner tree problem on the Server-Client model of computation.  ...  In particular, this work analyzes the time delays among server and clients for the parallel Steiner tree algorithm and examines some consequences of time delays on the execution time by considering constant  ...  Therefore, the Euclidean Steiner tree problem is at least as difficult as any NP-complete problem [3] .  ... 
doi:10.1109/itng.2008.167 dblp:conf/itng/Muhammad08a fatcat:5d57rcg76bcs3doflvcuahdffq

A Parallel Computation of the Steiner Tree Algorithm on Server-Client Paradigm

Rashid Bin Muhammad
2008 22nd International Conference on Advanced Information Networking and Applications - Workshops (aina workshops 2008)  
This paper presents the computational analysis of the Steiner tree problem on the Server-Client model of computation.  ...  In particular, this work analyzes the time delays among server and clients for the parallel Steiner tree algorithm and examines some consequences of time delays on the execution time by considering constant  ...  Therefore, the Euclidean Steiner tree problem is at least as difficult as any NP-complete problem [7] .  ... 
doi:10.1109/waina.2008.64 dblp:conf/aina/Muhammad08a fatcat:jo2uzrzw4feefd2jsaopotz42e

Steiner Minimal Trees: An Introduction, Parallel Computation, and Future Work [chapter]

Frederick C. Harris
1998 Handbook of Combinatorial Optimization  
This intriguing optimization problem is known as the Steiner Minimal Tree Problem (SMT), where the junctions that are added to the network are called Steiner Points.  ...  This chapter presents a brief overview of the problem, presents an approximation algorithm which performs very well, then reviews the computational algorithms implemented for this problem.  ...  Results indicate that 1) Warme's FST concatenation solved by branch-and-cut is orders of magnitude faster than backtrack search or dynamic programming based FST concatenation algorithms.; and 2) The Euclidean  ... 
doi:10.1007/978-1-4613-0303-9_13 fatcat:qwecvoftkvc7tkcfzq2xn77bqu

A Survey on Steiner Tree Construction and Global Routing for VLSI Design

Hao Tang, Genggeng Liu, Xiaohua Chen, Naixue Xiong
2020 IEEE Access  
Steiner tree construction is one of the basic models of VLSI physical design, which is usually used in the initial topology creation for noncritical nets in physical design.  ...  In a GR process, a Steiner Minimum Tree (SMT) algorithm can be invoked millions of times, which means that SMT algorithm has great significance for the final quality of GR.  ...  In Section III, we describe the problem model for the two problems of Steiner tree construction and GR.  ... 
doi:10.1109/access.2020.2986138 fatcat:nqpdbybucjembl4iztn67l4fgi

A General Approximation Technique for Constrained Forest Problems

Michel X. Goemans, David P. Williamson
1995 SIAM journal on computing (Print)  
Moreover, for the prize-collecting traveling salesman or Steiner tree problems, we obtain 2-approximation algorithms, therefore improving the previously best-known performance guarantees of 2.5 and 3,  ...  tree problems.  ...  For the Steiner tree problem, we obtain the minimum spanning tree heuristic whose many variants have been described in the literature (see [39] ).  ... 
doi:10.1137/s0097539793242618 fatcat:3t52ousxgvhrfjesjh5p6nptei

On Efficient Deployment of Wireless Sensors for Coverage and Connectivity in Constrained 3D Space

Chase Wu, Li Wang
2017 Sensors  
Extensive simulation results show that the proposed deployment algorithms consistently outperform the GA-based heuristic and achieve a close-to-optimal performance in small-scale problem instances and  ...  For performance comparison, we design and implement an optimal solution and a genetic algorithm (GA)-based approach.  ...  Wu formulated the problems and designed the algorithms and the experiments; L. Wang made contributions to the implementation and evaluation of the proposed algorithms.  ... 
doi:10.3390/s17102304 pmid:28994749 pmcid:PMC5677243 fatcat:tsgl3wctd5eipmfqneqqp277jy

Solving Dynamic Graph Problems with Multi-Attention Deep Reinforcement Learning [article]

Udesh Gunarathna, Renata Borovica-Gajic, Shanika Karunasekara, Egemen Tanin
2022 arXiv   pre-print
Graph problems such as traveling salesman problem, or finding minimal Steiner trees are widely studied and used in data engineering and computer science.  ...  However, most of the existing methods for learning heuristics focus on static graph problems.  ...  This is an NP-hard optimization problem, and can be reduced to a minimum Steiner tree [4] .  ... 
arXiv:2201.04895v1 fatcat:2sxtd5l3k5cl7dgfbkqzedi62q

Approximation algorithms for network design: A survey

Anupam Gupta, Jochen Könemann
2011 Surveys in Operations Research and Management Science  
The minimum spanning tree problem has been studied for at least a century, and it is clearly one of the most prominent network design problems.  ...  For example, we may wish to find a minimum-cost set of edges that induces a connected graph (this is the minimum-cost spanning tree problem), or we might want to find a minimum-cost set of arcs in a directed  ...  Perhaps the first application of the matching-based heuristic was for Christofides' 3 2 -approximation algorithm for the metric traveling salesman problem: we first find a minimum spanning tree (whose  ... 
doi:10.1016/j.sorms.2010.06.001 fatcat:l5dkgpvwlnh5bkmjhfhmmkqwoi

Edge sets: an effective evolutionary coding of spanning trees

G.R. Raidl, B.A. Julstrom
2003 IEEE Transactions on Evolutionary Computation  
The algorithm's operators are easily extended to generate only feasible spanning trees and to incorporate local, problem-specific heuristics.  ...  We demonstrate the usefulness of the edge-set encoding in an evolutionary algorithm for the NP-hard degree-constrained minimum spanning tree problem.  ...  Acknowledgments The authors would like to thank the anonymous reviewers and David Fogel for their their valueable comments on a previous version of this article.  ... 
doi:10.1109/tevc.2002.807275 fatcat:iaecjournrdanmcuukhqbajx2i
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