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Steiner trees have been extensively studied in the context of weighted graphs. The prototype is, arguably, the Steiner tree problem in graphs. Let G = (V, E) be an undirected graph with non-negative edge weights c and let S ⊆ V be a subset of vertices, called terminals. A Steiner tree is a tree in G that spans S.
In computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete.In his 1972 paper, "Reducibility Among Combinatorial Problems", [1] Richard Karp used Stephen Cook's 1971 theorem that the boolean satisfiability problem is NP-complete [2] (also called the Cook-Levin theorem) to show that there is a polynomial time many-one reduction ...
The goal of the Steiner tree problem is to connect these terminals by a tree whose weight is as small as possible. To transform this problem into an instance of the k-minimum spanning tree problem, Ravi et al. (1996) attach to each terminal a tree of zero-weight edges with a large number t of vertices per tree.
The single-trunk Steiner tree is a tree that consists of a single horizontal segment and some vertical segments. A minimum single-trunk Steiner tree (MSTST) may be found in O ( n log n ) time. However simply finding all its edges requires linear time .
Example of Steiner points (in red) added to a triangulation to improve the quality of triangles. In computational geometry, a Steiner point is a point that is not part of the input to a geometric optimization problem but is added during the solution of the problem, to create a better solution than would be possible from the original points alone.
The Steiner tree in graphs is not a generalisation but in fact a special case of the Steiner tree problem: The general case allows inclusion of Steiner points from a metric space (in the Euclidean case even a continuum), whereas the Steiner tree in graphs only from a weighted graph. A metric space with infinitely many points is not a graph, though.
The Fano plane is a Steiner triple system S(2,3,7). The blocks are the 7 lines, each containing 3 points. Every pair of points belongs to a unique line. In combinatorial mathematics, a Steiner system (named after Jakob Steiner) is a type of block design, specifically a t-design with λ = 1 and t = 2 or (recently) t ≥ 2.
The NFC wild-card game between the Los Angeles Rams and Minnesota Vikings is being moved to Arizona, the NFL announced Thursday. The game remains scheduled for Monday at 5 p.m. PT, but will now be ...
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