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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 ...
Graph homomorphism problem [3]: GT52 Graph partition into subgraphs of specific types (triangles, isomorphic subgraphs, Hamiltonian subgraphs, forests, perfect matchings) are known NP-complete. Partition into cliques is the same problem as coloring the complement of the given graph. A related problem is to find a partition that is optimal terms ...
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]
Set cover problem; Set packing; Set splitting problem; Set TSP problem; Shakashaka; Shared risk resource group; Shikaku; Shortest common supersequence; Single-machine scheduling; Skew-symmetric graph; Slitherlink; Slope number; Smallest grammar problem; Sokoban; Star coloring; Steiner tree problem; String graph; String-to-string correction ...
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.
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 ...
Examining the topology of the nodes and edges itself is another way to characterize networks. The distribution of degree of the nodes is often considered, regarding the structure of edges it is useful to find the Minimum spanning tree, or the generalization, the Steiner tree and the relative neighborhood graph.
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 ...