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In combinatorial mathematics, the Steiner tree problem, or minimum Steiner tree problem, named after Jakob Steiner, is an umbrella term for a class of problems in combinatorial optimization. While Steiner tree problems may be formulated in a number of settings, they all require an optimal interconnect for a given set of objects and a predefined ...
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]
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 ...
The Steiner ratio is the supremum, over all point sets, of the ratio of lengths of the Euclidean minimum spanning tree to the Steiner minimum tree. Because the Steiner minimum tree is shorter, this ratio is always greater than one. [2] A lower bound on the Steiner ratio is provided by three points at the vertices of an equilateral triangle of ...
The name of these points comes from the Steiner tree problem, named after Jakob Steiner, in which the goal is to connect the input points by a network of minimum total length. If the input points alone are used as endpoints of the network edges, then the shortest network is their minimum spanning tree. However, shorter networks can often be ...
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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.
Virtually every cell in the body requires iron in order to function well. Iron is involved in key bodily processes, including the transportation of oxygen in the blood. It also plays a central ...