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The general graph Steiner tree problem can be approximated by computing the minimum spanning tree of the subgraph of the metric closure of the graph induced by the terminal vertices, as first published in 1981 by Kou et al. [18] The metric closure of a graph G is the complete graph in which each edge is weighted by the shortest path distance ...
Minor testing (checking whether an input graph contains an input graph as a minor); the same holds with topological minors; Steiner tree, or Minimum spanning tree for a subset of the vertices of a graph. [2] (The minimum spanning tree for an entire graph is solvable in polynomial time.) Modularity maximization [5]
The RSMT is an NP-hard problem, and as with other NP-hard problems, common approaches to tackle it are approximate algorithms, heuristic algorithms, and separation of efficiently solvable special cases. An overview of the approaches to the problem may be found in the 1992 book by Hwang, Richards and Winter, The Steiner Tree Problem. [3]
English: A graph of the solution of the Steiner problem for 3 points in the Euclidean plane. Português: Um grafo para a solução do problema da árvore de Steiner com três pontos no plano euclidiano.
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.
Therefore, the k-minimum spanning tree must be formed by combining the optimal Steiner tree with enough of the zero-weight edges of the added trees to make the total tree size large enough. [ 2 ] Even for a graph whose edge weights belong to the set {1, 2, 3 }, testing whether the optimal solution value is less than a given threshold is NP ...
Download QR code; Print/export ... Pages in category "Computational problems in graph theory" ... Spanning tree; Steiner tree problem;
Outerplanar graph; Random graph; Regular graph; Scale-free network; Snark (graph theory) Sparse graph. Sparse graph code; Split graph; String graph; Strongly regular graph; Threshold graph; Total graph; Tree (graph theory). Trellis (graph) Turán graph; Ultrahomogeneous graph; Vertex-transitive graph; Visibility graph. Museum guard problem ...