• Thumbnail for Steiner tree problem
    mathematics, the Steiner tree problem, or minimum Steiner tree problem, named after Jakob Steiner, is an umbrella term for a class of problems in combinatorial...
    35 KB (4,388 words) - 13:27, 12 August 2024
  • Thumbnail for Steiner point (computational geometry)
    points alone. The name of these points comes from the Steiner tree problem, named after Jakob Steiner, in which the goal is to connect the input points by...
    2 KB (213 words) - 09:23, 7 June 2021
  • The rectilinear Steiner tree problem, minimum rectilinear Steiner tree problem (MRST), or rectilinear Steiner minimum tree problem (RSMT) is a variant...
    5 KB (719 words) - 03:56, 23 March 2024
  • Thumbnail for K-minimum spanning tree
    tree problem has been shown to be NP-hard by a reduction from the Steiner tree problem. The reduction takes as input an instance of the Steiner tree problem:...
    8 KB (1,057 words) - 10:20, 13 October 2024
  • mathematics, Steiner's problem (named after Jakob Steiner) may refer to: Steiner's calculus problem The Steiner tree problem Steiner's conic problem This disambiguation...
    189 bytes (53 words) - 19:53, 7 April 2016
  • approximation Variations of the Steiner tree problem. Specifically, with the discretized Euclidean metric, rectilinear metric. The problem is known to be NP-hard...
    29 KB (2,746 words) - 10:59, 2 November 2024
  • solution to the Steiner tree problem for those three vertices The Fermat point of a triangle, the solution to the Steiner tree problem for the three vertices...
    842 bytes (158 words) - 01:33, 30 March 2021
  • Winter, Dana; Winter, Pawel (1992). "The Steiner Tree Problem". Annals of Discrete Mathematics. DIMACS Steiner Tree Challenge Ruchansky, Natali; Bonchi, Francesco;...
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  • subsequent authors on the Steiner tree problem, e.g. Robins and Zelikovsky proposed an approximation algorithm for Steiner tree problem which on quasi-bipartite...
    4 KB (523 words) - 21:47, 25 August 2023
  • Thumbnail for K-tree
    ISBN 978-3-540-85218-6. Hwang, Frank; Richards, Dana; Winter, Pawel (1992), The Steiner Tree Problem, Annals of Discrete Mathematics (North-Holland Mathematics Studies)...
    5 KB (486 words) - 03:58, 25 September 2024
  • Thumbnail for Physarum polycephalum
    compute shortest paths. A very similar model can be shown to solve the Steiner tree problem. However, these models are externally consistent but not internally...
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  • Thumbnail for Minimum spanning tree
    Hamiltonian cycle. The Steiner tree of a subset of the vertices is the minimum tree that spans the given subset. Finding the Steiner tree is NP-Complete. The...
    44 KB (5,460 words) - 21:16, 9 October 2024
  • Thumbnail for Euclidean minimum spanning tree
    form, forming a tree with smaller total length. In comparison, the Steiner tree problem has a stronger angle bound: an optimal Steiner tree has all angles...
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  • the optimum solution, the problem is W[2]-hard (due to a folklore reduction from the Dominating Set problem). Steiner Tree is also known to be APX-hard...
    28 KB (3,354 words) - 12:49, 29 July 2024
  • Thumbnail for Vera Traub
    algorithms for combinatorial optimization problems including the travelling salesperson problem and the Steiner tree problem. She is a junior professor in the...
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  • Thumbnail for Time complexity
    arise in approximation algorithms; a famous example is the directed Steiner tree problem, for which there is a quasi-polynomial time approximation algorithm...
    41 KB (4,998 words) - 15:48, 2 November 2024
  • Thumbnail for Vertex cover
    2010-03-05. Garey, Michael R.; Johnson, David S. (1977). "The rectilinear Steiner tree problem is NP-complete". SIAM Journal on Applied Mathematics. 32 (4): 826–834...
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  • centered decagonal number. For the Steiner tree problem, 31 is the number of possible Steiner topologies for Steiner trees with 4 terminals. At 31, the Mertens...
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  • undirected graphs, for formulating the Steiner tree problem on networks, and for his work on facility location problems on networks. Hakimi, S. L. (1963),...
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  • Thumbnail for Greedy algorithm
    Other problems for which the greedy algorithm gives a strong guarantee, but not an optimal solution, include Set cover The Steiner tree problem Load balancing...
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  • Almost every problem associated with routing is known to be intractable. The simplest routing problem, called the Steiner tree problem, of finding the...
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  • Thumbnail for Fermat point
    The Fermat point gives a solution to the geometric median and Steiner tree problems for three points. The Fermat point of a triangle with largest angle...
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  • Thumbnail for Hanan grid
    Hanan Grid Problems Networks, vol. 38, 2000, pp. 200-221 Christine R. Leverenz, Miroslaw Truszczynski, The Rectilinear Steiner Tree Problem: Algorithms...
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  • Miloš Kössler [cs] (1934) on the Euclidean Steiner tree problem. In this problem, one must again form a tree connecting a given set of points, with edge...
    20 KB (2,201 words) - 20:44, 8 October 2024
  • spanning tree is a spanning tree where the maximum vertex degree is limited to a certain constant k. The degree-constrained spanning tree problem is to determine...
    3 KB (374 words) - 00:46, 30 November 2020
  • minimum Steiner tree problem with an approximation ratio 1.55, widely cited by his peers and also widely held in libraries. "Improved Steiner Tree Approximation...
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  • are able to memorize mazes. It is proposed as a solution to the Steiner tree problem to figure out the shortest path between two points. Additionally...
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  • Thumbnail for Bipartite graph
    two points have the same parity Quasi-bipartite graph, a type of Steiner tree problem instance in which the terminals form an independent set, allowing...
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  • the bond percolation problem then there must be a giant component in the RGG. Gilbert did important work on the Steiner tree problem in 1968, formulating...
    16 KB (1,730 words) - 07:10, 6 May 2024
  • Thumbnail for Jakob Steiner
    symmetrization Steiner system Steiner surface Steiner conic Steiner's conic problem Steiner's problem Steiner tree Steiner chain Poncelet–Steiner theorem Parallel...
    9 KB (1,003 words) - 23:49, 25 September 2024