Algorithms for the power-p Steiner tree problem in the Euclidean plane
نویسندگان
چکیده
منابع مشابه
Algorithms for the power-p Steiner tree problem in the Euclidean plane
We study the problem of constructing minimum power-p Euclidean k-Steiner trees in the plane. The problem is to find a tree of minimum cost spanning a set of given terminals where, as opposed to the minimum spanning tree problem, at most k additional nodes (Steiner points) may be introduced anywhere in the plane. The cost of an edge is its length to the power of p (where p ≥ 1), and the cost of ...
متن کاملInapproximability of the Euclidean power-p Steiner tree problem
For a real number p ≥ 2, an integer k > 0 and a set of terminals X in the plane, the Euclidean power-p Steiner tree problem asks for a tree interconnecting X and at most k Steiner points such that the sum of the p-th powers of the edge lengths is minimised. We show that this problem is in the complexity subclass exp-APX (but not poly-APX) of NPO. We then demonstrate that the approximation algor...
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Most heuristics for the Steiner tree problem in the Euclidean plane perform a series of iterative improvements using the minimum spanning tree as an initial solution. We may therefore characterize them as local search heuristics. In this paper, we rst give a survey of existing heuristic approaches from a local search perspective, by setting up solution spaces and neighbourhood structures. Secon...
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The Euclidean Steiner tree problem is solved by finding the tree with minimal Euclidean length spanning a set of fixed vertices in the plane, while allowing for the addition of auxiliary vertices (Steiner vertices). Steiner trees are widely used to design real-world structures like highways and oil pipelines. Unfortunately, the Euclidean Steiner Tree Problem has shown to be NP-Hard, meaning the...
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Most heuristics for the Steiner tree problem in the Euclidean plane perform a series of iterative improvements using the minimum spanning tree as an initial solution. We may therefore characterize them as local search heuristics. In this paper, we ®rst give a survey of existing heuristic approaches from a local search perspective, by setting up solution spaces and neighbourhood structures. Seco...
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ژورنال
عنوان ژورنال: Revista de Informática Teórica e Aplicada
سال: 2018
ISSN: 2175-2745,0103-4308
DOI: 10.22456/2175-2745.80525