Relevant bibliographies by topics / Steiner problem

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Steiner problem'

Author: Grafiati
Published: 4 June 2021
Last updated: 21 February 2023

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Journal articles on the topic "Steiner problem"

1

Weng, Jia Feng. "Steiner polygons in the Steiner problem." Geometriae Dedicata 52, no. 2 (September 1994): 119–27. http://dx.doi.org/10.1007/bf01263600.

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Sharma, Gokarna, and Costas Busch. "The Bursty Steiner Tree Problem." International Journal of Foundations of Computer Science 28, no. 07 (November 2017): 869–87. http://dx.doi.org/10.1142/s0129054117500290.

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We introduce and study a new Steiner tree problem variation called the bursty Steiner tree problem where new nodes arrive into bursts. This is an online problem which becomes the well-known online Steiner tree problem if the number of nodes in each burst is exactly one and becomes the classic Steiner tree problem if all the nodes appear in a single burst. In undirected graphs, we provide a tight bound of [Formula: see text] on the competitive ratio for this problem, where [Formula: see text] is the total number of nodes to be connected and [Formula: see text] is the total number of different bursts. In directed graphs of bounded edge asymmetry [Formula: see text], we provide a competitive ratio for this problem with a gap of [Formula: see text] factor between the lower bound and the upper bound. We also show that a tight bound of [Formula: see text] on the competitive ratio can be obtained for a bursty variation of the terminal Steiner tree problem. These are the first results that provide clear performance trade-offs for a novel Steiner tree problem variation that subsumes both of its online and classic versions.
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Vujosevic, Mirko, and Milan Stanojevic. "A bicriterion Steiner tree problem on graph." Yugoslav Journal of Operations Research 13, no. 1 (2003): 25–33. http://dx.doi.org/10.2298/yjor0301025v.

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This paper presents a formulation of bicriterion Steiner tree problem which is stated as a task of finding a Steiner tree with maximal capacity and minimal length. It is considered as a lexicographic multicriteria problem. This means that the bottleneck Steiner tree problem is solved first. After that, the next optimization problem is stated as a classical minimums Steiner tree problem under the constraint on capacity of the tree. The paper also presents some computational experiments with the multicriteria problem.
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Chen, Yen Hung. "The Clustered Selected-Internal Steiner Tree Problem." International Journal of Foundations of Computer Science 33, no. 01 (November 30, 2021): 55–66. http://dx.doi.org/10.1142/s0129054121500362.

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Given a complete graph [Formula: see text], with nonnegative edge costs, two subsets [Formula: see text] and [Formula: see text], a partition [Formula: see text] of [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] of [Formula: see text], [Formula: see text], a clustered Steiner tree is a tree [Formula: see text] of [Formula: see text] that spans all vertices in [Formula: see text] such that [Formula: see text] can be cut into [Formula: see text] subtrees [Formula: see text] by removing [Formula: see text] edges and each subtree [Formula: see text] spans all vertices in [Formula: see text], [Formula: see text]. The cost of a clustered Steiner tree is defined to be the sum of the costs of all its edges. A clustered selected-internal Steiner tree of [Formula: see text] is a clustered Steiner tree for [Formula: see text] if all vertices in [Formula: see text] are internal vertices of [Formula: see text]. The clustered selected-internal Steiner tree problem is concerned with the determination of a clustered selected-internal Steiner tree [Formula: see text] for [Formula: see text] and [Formula: see text] in [Formula: see text] with minimum cost. In this paper, we present the first known approximation algorithm with performance ratio [Formula: see text] for the clustered selected-internal Steiner tree problem, where [Formula: see text] is the best-known performance ratio for the Steiner tree problem.
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Gueron, Shay, and Ran Tessler. "The Fermat-Steiner Problem." American Mathematical Monthly 109, no. 5 (May 2002): 443. http://dx.doi.org/10.2307/2695644.

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Imase, Makoto, and Bernard M. Waxman. "Dynamic Steiner Tree Problem." SIAM Journal on Discrete Mathematics 4, no. 3 (August 1991): 369–84. http://dx.doi.org/10.1137/0404033.

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Borndörfer, Ralf, Marika Karbstein, and Marc E. Pfetsch. "The Steiner connectivity problem." Mathematical Programming 142, no. 1-2 (June 8, 2012): 133–67. http://dx.doi.org/10.1007/s10107-012-0564-5.

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Gueron, Shay, and Ran Tessler. "The Fermat-Steiner Problem." American Mathematical Monthly 109, no. 5 (May 2002): 443–51. http://dx.doi.org/10.1080/00029890.2002.11919871.

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van Oudheusden, Dirk. "The Steiner tree problem." European Journal of Operational Research 81, no. 1 (February 1995): 221. http://dx.doi.org/10.1016/0377-2217(95)90155-8.

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WENG, J. F., I. MAREELS, and D. A. THOMAS. "COMPUTING STEINER POINTS AND PROBABILITY STEINER POINTS IN ℓ1 AND ℓ2 METRIC SPACES." Discrete Mathematics, Algorithms and Applications 01, no. 04 (December 2009): 541–54. http://dx.doi.org/10.1142/s1793830909000403.

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The Steiner tree problem is a well known network optimization problem which asks for a connected minimum network (called a Steiner minimum tree) spanning a given point set N. In the original Steiner tree problem the given points lie in the Euclidean plane or space, and the problem has many variants in different applications now. Recently a new type of Steiner minimum tree, probability Steiner minimum tree, is introduced by the authors in the study of phylogenies. A Steiner tree is a probability Steiner tree if all points in the tree are probability vectors in a vector space. The points in a Steiner minimum tree (or a probability Steiner tree) that are not in the given point set are called Steiner points (or probability Steiner points respectively). In this paper we investigate the properties of Steiner points and probability Steiner points, and derive the formulae for computing Steiner points and probability Steiner points in ℓ1- and ℓ2-metric spaces. Moreover, we show by an example that the length of a probability Steiner tree on 3 points and the probability Steiner point in the tree are smooth functions with respect to p in d-space.
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Dissertations / Theses on the topic "Steiner problem"

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Alex, Jerome. "The periodic Steiner problem." Phd thesis, Technische Universität Darmstadt, 2019. http://tuprints.ulb.tu-darmstadt.de/8538/1/AlexDiss.pdf.

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We study a problem of geometric graph theory: We determine the triply periodic graph in Euclidean 3-space which minimizes length among all graphs spanning a fundamental domain of 3-space with the same volume. This problem is related to minimizing the Willmore energy of triply periodic surfaces under a volume constraint.
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Minkoff, Maria 1976. "The Prize Collecting Steiner Tree problem." Thesis, Massachusetts Institute of Technology, 2000. http://hdl.handle.net/1721.1/86544.

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Swanepoel, Konrad Johann. "The local Steiner problem in Minkowski spaces." Doctoral thesis, Universitätsbibliothek Chemnitz, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-201000873.

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The subject of this monograph can be described as the local properties of geometric Steiner minimal trees in finite-dimensional normed spaces. A Steiner minimal tree of a finite set of points is a shortest connected set interconnecting the points. For a quick introduction to this topic and an overview of all the results presented in this work, see Chapter 1. The relevant mathematical background knowledge needed to understand the results and their proofs are collected in Chapter 2. In Chapter 3 we introduce the Fermat-Torricelli problem, which is that of finding a point that minimizes the sum of distances to a finite set of given points. We only develop that part of the theory of Fermat-Torricelli points that is needed in later chapters. Steiner minimal trees in finite-dimensional normed spaces are introduced in Chapter 4, where the local Steiner problem is given an exact formulation. In Chapter 5 we solve the local Steiner problem for all two-dimensional spaces, and generalize this solution to a certain class of higher-dimensional spaces (CL spaces). The twodimensional solution is then applied to many specific norms in Chapter 6. Chapter 7 contains an abstract solution valid in any dimension, based on the subdifferential calculus. This solution is applied to two specific high-dimensional spaces in Chapter 8. In Chapter 9 we introduce an alternative approach to bounding the maximum degree of Steiner minimal trees from above, based on the illumination problem from combinatorial convexity. Finally, in Chapter 10 we consider the related k-Steiner minimal trees, which are shortest Steiner trees in which the number of Steiner points is restricted to be at most k
Das Thema dieser Habilitationsschrift kann als die lokalen Eigenschaften der geometrischen minimalen Steiner-Bäume in endlich-dimensionalen normierten Räumen beschrieben werden. Ein minimaler Steiner-Baum einer endlichen Punktmenge ist eine kürzeste zusammenhängende Menge die die Punktmenge verbindet. Kapitel 1 enthält eine kurze Einführung zu diesem Thema und einen Überblick über alle Ergebnisse dieser Arbeit. Die entsprechenden mathematischen Vorkenntnisse mit ihren Beweisen, die erforderlich sind die Ergebnisse zu verstehen, erscheinen in Kapitel 2. In Kapitel 3 führen wir das Fermat-Torricelli-Problem ein, das heißt, die Suche nach einem Punkt, der die Summe der Entfernungen der Punkte einer endlichen Punktmenge minimiert. Wir entwickeln nur den Teil der Theorie der Fermat-Torricelli-Punkte, der in späteren Kapiteln benötigt wird. Minimale Steiner-Bäume in endlich-dimensionalen normierten Räumen werden in Kapitel 4 eingeführt, und eine exakte Formulierung wird für das lokale Steiner-Problem gegeben. In Kapitel 5 lösen wir das lokale Steiner-Problem für alle zwei-dimensionalen Räume, und diese Lösung wird für eine bestimmte Klasse von höher-dimensionalen Räumen (den sog. CL-Räumen) verallgemeinert. Die zweidimensionale Lösung wird dann auf mehrere bestimmte Normen in Kapitel 6 angewandt. Kapitel 7 enthält eine abstrakte Lösung die in jeder Dimension gilt, die auf der Analysis von Subdifferentialen basiert. Diese Lösung wird auf zwei bestimmte höher-dimensionale Räume in Kapitel 8 angewandt. In Kapitel 9 führen wir einen alternativen Ansatz zur oberen Schranke des maximalen Grads eines minimalen Steiner-Baums ein, der auf dem Beleuchtungsproblem der kombinatorischen Konvexität basiert ist. Schließlich betrachten wir in Kapitel 10 die verwandten minimalen k-Steiner-Bäume. Diese sind die kürzesten Steiner-Bäume, in denen die Anzahl der Steiner-Punkte auf höchstens k beschränkt wird
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Wang, Xinhui. "Exact algorithms for the Steiner tree problem." Enschede : University of Twente [Host], 2008. http://doc.utwente.nl/59035.

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Srinivasan, Sangeetha Rodger C. A. "Disjoint Intersection problem For Steiner triple systems." Auburn, Ala., 2007. http://repo.lib.auburn.edu/2007%20Fall%20Theses/Srinivasan_Sangeetha_36.pdf.

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Vahdati-Daneshmand, Siavash. "Algorithmic approaches to the Steiner problem in networks." [S.l. : s.n.], 2004. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB11051778.

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Mussafi, Noor Saif Muhammad. "Complexity and Approximation of the Rectilinear Steiner Tree Problem." Master's thesis, Universitätsbibliothek Chemnitz, 2009. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200901213.

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Given a finite set K of terminals in the plane. A rectilinear Steiner minimum tree for K (RST) is a tree which interconnects among these terminals using only horizontal and vertical lines of shortest possible length containing Steiner point. We show the complexity of RST i.e. belongs to NP-complete. Moreover we present an approximative method of determining the solution of RST problem proposed by Sanjeev Arora in 1996, Arora's Approximation Scheme. This algorithm has time complexity polynomial in the number of terminals for a fixed performance ratio 1 + Epsilon.
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Logan, Andrew. "The Steiner Problem on Closed Surfaces of Constant Curvature." BYU ScholarsArchive, 2015. https://scholarsarchive.byu.edu/etd/4420.

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The n-point Steiner problem in the Euclidean plane is to find a least length path network connecting n points. In this thesis we will demonstrate how to find a least length path network T connecting n points on a closed 2-dimensional Riemannian surface of constant curvature by determining a region in the covering space that is guaranteed to contain T. We will then provide an algorithm for solving the n-point Steiner problem on such a surface.
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Van, Laarhoven Jon William. "Exact and heuristic algorithms for the Euclidean Steiner tree problem." Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/755.

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In this thesis, we study the Euclidean Steiner tree problem (ESTP) which arises in the field of combinatorial optimization. The ESTP asks for a network of minimal total edge length spanning a set of given terminal points in Rd with the ability to add auxiliary connecting points (Steiner points) to decrease the overall length of the network. The graph theory literature contains extensive studies of exact, approximation, and heuristic algorithms for ESTP in the plane, but less is known in higher dimensions. The contributions of this thesis include a heuristic algorithm and enhancements to an exact algorithm for solving the ESTP. We present a local search heuristic for the ESTP in Rd for d ≥ 2. The algorithm utilizes the Delaunay triangulation to generate candidate Steiner points for insertion, the minimum spanning tree to create a network on the inserted points, and second order cone programming to optimize the locations of Steiner points. Unlike other ESTP heuristics relying on the Delaunay triangulation, the algorithm inserts Steiner points probabilistically into Delaunay triangles to achieve different subtrees on subsets of terminal points. The algorithm extends effectively into higher dimensions, and we present computational results on benchmark test problems in Rd for 2 ≤ d ≤ 5. We develop new geometric conditions derived from properties of Steiner trees which bound below the number of Steiner points on paths between terminals in the Steiner minimal tree. We describe conditions for trees with a Steiner topology and show how these conditions relate to the Voronoi diagram. We describe more restrictive conditions for trees with a full Steiner topology and their implementation into the algorithm of Smith (1992). We present computational results on benchmark test problems in Rd for 2 ≤ d ≤ 5.
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Cinel, Sertac. "Sequential And Parallel Heuristic Algorithms For The Rectilinear Steiner Tree Problem." Master's thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/12607896/index.pdf.

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The Steiner Tree problem is one of the most popular graph problems and has many application areas. The rectilinear version of this problem, introduced by Hanan, has taken special attention since it addresses a fundamental matter in &ldquo
Physical Design&rdquo
phase of the Very Large Scale Integrated (VLSI) Computer Aided Design (CAD) process. The Rectilinear Steiner Tree Problem asks for a minimum length tree that interconnects a given set of points by only horizontal and vertical line segments, enabling the use of extra points. There are various exact algorithms. However the problem is NP-complete hence approximation algorithms have to be used especially for large instances. In this thesis work, first a survey on heuristics for the Rectilinear Steiner Tree Problem is conducted and then two recently developed successful algorithms, BGA by Kahng et. al. and RST by Zhou have been studied and investigated deeply. Both algorithms have subproblems, most of which have individual backgrounds in literature. After an analysis of BGA and RST, the thesis proposes a modification on RST, which leads to a faster and non-recursive version. The efficiency of the modified algorithm has been validated by computational tests using both random and VLSI benchmark instances. A partially parallelized version of the modified algorithm is also proposed for distributed computing environments. It is implemented using MPI (message passing interface) middleware and the results of comparative tests conducted on a cluster of workstations are presented. The proposed distributed algorithm has also proved to be promising especially for large problem instances.
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Books on the topic "Steiner problem"

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Hwang, Frank. The Steiner tree problem. Amsterdam: North-Holland, 1992.

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Hwang, Frank K. The Steiner tree problem. London: North-Holland, 1992.

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Prömel, Hans Jürgen, and Angelika Steger. The Steiner Tree Problem. Wiesbaden: Vieweg+Teubner Verlag, 2002. http://dx.doi.org/10.1007/978-3-322-80291-0.

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Ivanov, A. O. Minimal networks: The Steiner problem and its generalizations. Boca Raton, Fla: CRC Press, 1994.

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Dror, Moshe. Directed Steiner tree problem on a graph: Models, relaxations, and algorithms. Monterey, Calif: Naval Postgraduate School, 1988.

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Voss, Stefan. Steiner-Probleme in Graphen. Frankfurt am Main: Anton Hain, 1990.

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Xiaodong, Hu, ed. Steiner tree problems in computer communication networks. Hackensack, NJ: World Scientific, 2008.

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Education and beyond: Steiner and the problems of modern society. Edinburgh: Floris Books, 1996.

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C, Menz Fredric, and Lipsey Richard G. 1928-, eds. Study guide and problems to accompany Economics, eighth edition, [by] Lipsey/Steiner/Purvis. New York: Harper & Row, 1987.

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Forbush, Dascomb Ramsey. Study guide and problems to accompany Economics, eighth edition, [by] Lipsey/Steiner/Purvis. New York: Harper & Row, 1987.

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Book chapters on the topic "Steiner problem"

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Lau, H. T. "Steiner Tree Problem." In Lecture Notes in Economics and Mathematical Systems, 81–97. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-642-61649-5_5.

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Prömel, Hans Jürgen, and Angelika Steger. "Geometric Steiner Problems." In The Steiner Tree Problem, 191–222. Wiesbaden: Vieweg+Teubner Verlag, 2002. http://dx.doi.org/10.1007/978-3-322-80291-0_10.

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Prömel, Hans Jürgen, and Angelika Steger. "Basics I: Graphs." In The Steiner Tree Problem, 1–22. Wiesbaden: Vieweg+Teubner Verlag, 2002. http://dx.doi.org/10.1007/978-3-322-80291-0_1.

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Prömel, Hans Jürgen, and Angelika Steger. "Basics II: Algorithms." In The Steiner Tree Problem, 23–40. Wiesbaden: Vieweg+Teubner Verlag, 2002. http://dx.doi.org/10.1007/978-3-322-80291-0_2.

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Prömel, Hans Jürgen, and Angelika Steger. "Basics III: Complexity." In The Steiner Tree Problem, 41–62. Wiesbaden: Vieweg+Teubner Verlag, 2002. http://dx.doi.org/10.1007/978-3-322-80291-0_3.

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Prömel, Hans Jürgen, and Angelika Steger. "Special Terminal Sets." In The Steiner Tree Problem, 63–74. Wiesbaden: Vieweg+Teubner Verlag, 2002. http://dx.doi.org/10.1007/978-3-322-80291-0_4.

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Prömel, Hans Jürgen, and Angelika Steger. "Exact Algorithms." In The Steiner Tree Problem, 75–86. Wiesbaden: Vieweg+Teubner Verlag, 2002. http://dx.doi.org/10.1007/978-3-322-80291-0_5.

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Prömel, Hans Jürgen, and Angelika Steger. "Approximation Algorithms." In The Steiner Tree Problem, 87–106. Wiesbaden: Vieweg+Teubner Verlag, 2002. http://dx.doi.org/10.1007/978-3-322-80291-0_6.

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Prömel, Hans Jürgen, and Angelika Steger. "More on Approximation Algorithms." In The Steiner Tree Problem, 107–32. Wiesbaden: Vieweg+Teubner Verlag, 2002. http://dx.doi.org/10.1007/978-3-322-80291-0_7.

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Prömel, Hans Jürgen, and Angelika Steger. "Randomness Helps." In The Steiner Tree Problem, 133–64. Wiesbaden: Vieweg+Teubner Verlag, 2002. http://dx.doi.org/10.1007/978-3-322-80291-0_8.

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Conference papers on the topic "Steiner problem"

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Oliveira, Andrey, Danilo Sanches, and Bruna Osti. "Hybrid greedy genetic algorithm for the Euclidean Steiner tree problem." In Encontro Nacional de Inteligência Artificial e Computacional. Sociedade Brasileira de Computação - SBC, 2019. http://dx.doi.org/10.5753/eniac.2019.9350.

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This paper presents a genetic algorithm for the Euclidean Steiner tree problem. This is an optimization problem whose objective is to obtain a minimum length tree to interconnect a set of fixed points, and for this purpose to be achieved, new auxiliary points, called Steiner points, can be added. The proposed heuristic uses a genetic algorithm to manipulate spanning trees, which are then transformed into Steiner trees by inserting and repositioning the Steiner points. Greedy genetic operators and evolutionary strategies are tested. Results of numerical experiments for benchmark library problem (OR-Library) are presented and discussed.This paper presents a genetic algorithm for the Euclidean Steiner tree problem. This is an optimization problem whose objective is to obtain a minimum length tree to interconnect a set of fixed points, and for this purpose to be achieved, new auxiliary points, called Steiner points, can be added. The proposed heuristic uses a genetic algorithm to manipulate spanning trees, which are then transformed into Steiner trees by inserting and repositioning the Steiner points. Greedy genetic operators and evolutionary strategies are tested. Results of numerical experiments for benchmark library problem (OR-Library) are presented and discussed.
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Leverenz, Christine R., and Miroslaw Truszczynski. "The rectilinear Steiner tree problem." In the 37th annual Southeast regional conference (CD-ROM). New York, New York, USA: ACM Press, 1999. http://dx.doi.org/10.1145/306363.306402.

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Park, Joon-Sang, Won W. Ro, Handuck Lee, and Neungsoo Park. "Parallel Algorithms for Steiner Tree Problem." In 2008 Third International Conference on Convergence and Hybrid Information Technology (ICCIT). IEEE, 2008. http://dx.doi.org/10.1109/iccit.2008.167.

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Abu-Affash, A. Karim, Paz Carmi, Matthew J. Katz, and Michael Segal. "The euclidean bottleneck steiner path problem." In the 27th annual ACM symposium. New York, New York, USA: ACM Press, 2011. http://dx.doi.org/10.1145/1998196.1998268.

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Hartley, Stephen J. "Steiner systems and the Boolean satisfiability problem." In the 1996 ACM symposium. New York, New York, USA: ACM Press, 1996. http://dx.doi.org/10.1145/331119.331192.

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Hsieh, Sun-Yuan, and Wen-Hao Pi. "On the Partial-Terminal Steiner Tree Problem." In 2008 International Symposium on parallel Architectures, Algorighms and Networks I-SPAN. IEEE, 2008. http://dx.doi.org/10.1109/i-span.2008.11.

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Guo, Longkun, Kewen Liao, and Hong Shen. "On the Shallow-Light Steiner Tree Problem." In 2014 15th International Conference on Parallel and Distributed Computing, Applications and Technologies (PDCAT). IEEE, 2014. http://dx.doi.org/10.1109/pdcat.2014.17.

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Noferesti, Samira, and Mehri Rajayi. "Solving Steiner Tree Problem by Using Learning Automata." In 2009 International Conference on Computational Intelligence and Software Engineering. IEEE, 2009. http://dx.doi.org/10.1109/cise.2009.5365407.

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Abu-Affash, A. Karim. "On the euclidean bottleneck full Steiner tree problem." In the 27th annual ACM symposium. New York, New York, USA: ACM Press, 2011. http://dx.doi.org/10.1145/1998196.1998267.

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Coric, Rebeka, Mateja Dumic, and Slobodan Jelic. "A genetic algorithm for Group Steiner Tree Problem." In 2018 41st International Convention on Information and Communication Technology, Electronics and Microelectronics (MIPRO). IEEE, 2018. http://dx.doi.org/10.23919/mipro.2018.8400173.

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Reports on the topic "Steiner problem"

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Dror, Moshe, Bezalel Gavish, and Jean Choquette. Directed Steiner Tree Problem on a Graph: Models, Relaxations, and Algorithms. Fort Belvoir, VA: Defense Technical Information Center, August 1988. http://dx.doi.org/10.21236/ada199769.

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