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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 ...
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] Monochromatic triangle [3]: GT6 Pathwidth, [6] or, equivalently, interval thickness, and vertex separation number [7] Rank coloring; k-Chinese postman
In the mathematical field of graph theory, an instance of the Steiner tree problem (consisting of an undirected graph G and a set R of terminal vertices that must be connected to each other) is said to be quasi-bipartite if the non-terminal vertices in G form an independent set, i.e. if every edge is incident on at least one terminal.
Download as PDF; Printable version; ... [7] and Steiner tree problems. [8] ... Although hypergraphs are more difficult to draw on paper than graphs, several ...
Almost every problem associated with routing is known to be intractable. The simplest routing problem, called the Steiner tree problem, of finding the shortest route for one net in one layer with no obstacles and no design rules is known to be NP-complete , both in the case where all angles are allowed or if routing is restricted to only ...
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]
Learn how to download and install or uninstall the Desktop Gold software and if your computer meets the system requirements.
In the Euclidean traveling salesperson path problem, the connecting line segments must start and end at the given points, like the spanning tree and unlike the Steiner tree; additionally, each point can touch at most two line segments, so the result forms a polygonal chain. Because of this restriction, the optimal path may be longer than the ...