A decomposition theorem on Euclidean Steiner minimal trees
نویسندگان
چکیده
منابع مشابه
Approximate Euclidean Steiner Trees
An approximate Steiner tree is a Steiner tree on a given set of terminals in Euclidean space such that the angles at the Steiner points are within a specified error from 120◦. This notion arises in numerical approximations of minimum Steiner trees. We investigate theworst-case relative error of the length of an approximate Steiner tree compared to the shortest tree with the same topology. It ha...
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In this paper, we propose modifications on Smith’s branch-and-bound (B&B) algorithm for the Euclidean Steiner problem in R. At each node of the B&B tree, we solve a convex programming problem in conic form to obtain a lower bound on the minimal Steiner tree length for a given topology. We also use conic formulation to obtain bounds on the child problems at a given node, that are applied on a st...
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While a spanning tree spans all vertices of a given graph, a Steiner tree spans a given subset of vertices. In the Steiner minimal tree problem, the vertices are divided into two parts: terminals and nonterminal vertices. The terminals are the given vertices which must be included in the solution. The cost of a Steiner tree is defined as the total edge weight. A Steiner tree may contain some no...
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Given a set V of size N 4 vertices in a metric space, how can one interconnect them with the possible use of a set S of size M vertices not in the set V , but in the same metric space, so that the cumulative cost of the inter-connections between all the vertices is a minimum? When one uses the Euclidean metric to compute these inter-connections, this is referred to as the Euclidean Steiner Mini...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1988
ISSN: 0179-5376,1432-0444
DOI: 10.1007/bf02187919