"RIV/00216305:26210/08:PU76870!RIV10-MSM-26210___" . . "26210" . "2008-06-18+02:00"^^ . "Brno" . . "[A3EF6DBDB1E3]" . . "RIV/00216305:26210/08:PU76870" . . . "Solving the Euclidean Steiner Tree Problem Using Geometric Structures" . "395865" . "8"^^ . "1"^^ . "Brno University of Technology" . "Proceedings of the 14th International Conference on Soft Computing MENDEL 2008" . . "1"^^ . "Solving the Euclidean Steiner Tree Problem Using Geometric Structures"@en . "Z(MSM0021630529)" . "The Euclidean Steiner Tree Problem is to find a shortest network spanning a set of fixed points in the plane, allowing the addition of auxiliary points to the set. The problem being NP-hard, polynomial-time approximations or heuristics are required. There are many rather complex heuristics based, e.g., on enumerating full topologies and consuming long time for computations for large instances. In this paper, we applied to use tools of computational geometry, especially the properties of Delaunay triangulation, a well-known geometric structure, and combine them with insertion heuristics based on the construction of the Euclidean minimum spanning tree. Thus an algorithm could be proposed that is very efficient and fast. Experiments confirmed that computations by this algorithm generate very good results in a reasonable amount of time, even for large instances of the studied problem." . . . . . "Solving the Euclidean Steiner Tree Problem Using Geometric Structures" . "Vysok\u00E9 u\u010Den\u00ED technick\u00E9 v Brn\u011B. Fakulta strojn\u00EDho in\u017Een\u00FDrstv\u00ED" . . "Solving the Euclidean Steiner Tree Problem Using Geometric Structures"@en . "978-80-214-3675-6" . "\u0160eda, Milo\u0161" . "The Euclidean Steiner Tree Problem is to find a shortest network spanning a set of fixed points in the plane, allowing the addition of auxiliary points to the set. The problem being NP-hard, polynomial-time approximations or heuristics are required. There are many rather complex heuristics based, e.g., on enumerating full topologies and consuming long time for computations for large instances. In this paper, we applied to use tools of computational geometry, especially the properties of Delaunay triangulation, a well-known geometric structure, and combine them with insertion heuristics based on the construction of the Euclidean minimum spanning tree. Thus an algorithm could be proposed that is very efficient and fast. Experiments confirmed that computations by this algorithm generate very good results in a reasonable amount of time, even for large instances of the studied problem."@en . . . "Steiner tree, Steiner ratio, heuristic, Delaunay triangulation"@en . . . . .