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The original problem was stated in the form that has become known as the Euclidean Steiner tree problem or geometric Steiner tree problem: Given N points in the plane, the goal is to connect them by lines of minimum total length in such a way that any two points may be interconnected by line segments either directly or via other points and line ...
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]
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 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.
A minimum spanning tree of a weighted planar graph.Finding a minimum spanning tree is a common problem involving combinatorial optimization. Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, [1] where the set of feasible solutions is discrete or can be reduced to a discrete set.
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 combinatorial optimization, the minimum Wiener connector problem is the problem of finding the minimum Wiener connector. It can be thought of as a version of the classic Steiner tree problem (one of Karp's 21 NP-complete problems), where instead of minimizing the size of the tree, the objective is to minimize the distances in the subgraph ...