Variational approach and Steiner minimal trees on four points
نویسندگان
چکیده
منابع مشابه
Steiner Minimal Trees ∗
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 finite set of points P in the Euclidean plane, the Steiner problem asks us to constuct a shortest possible network interconnecting P. Such a network is known as a minimal Steiner tree. The Steiner problem is an intrinsically difficult one, having been shown to be NP-hard [7]; however, it often proves far more tractable if we restrict our attention to points in special geometric configur...
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Given n terminals in the Euclidean plane and a positive constant, find a Steiner tree interconnecting all terminals with the minimum number of Steiner points such that the Euclidean length of each edge is no more than the given positive constant. This problem is NP-hard with applications in VLSI design, WDM optical networks and wireless communications. In this paper, we show that (a) the Steine...
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An O(n log n) time and O(n) space algorithm for the Euclidean Steiner tree problem with four terminals in a simple polygon with n vertices is given. Its applicability to the problem of determining good quality solutions for any number of terminals is discussed.
متن کاملSteiner minimal trees on the union of two orthogonal rectangles
Suppose R is a union of two subsets Rl and R2 whose Steiner minimal trees SMT(R 1) and SMT(R2) are known. The decomposition question is when the Steiner minimal tree SMT(R) for R is just the union of two Steiner minimal trees on R 1 and R2 In this paper a special case studied, that R 1 =bcda, R2=defg are two non-overlapping rectangles with a common vertex d so that a,d,e lie on one line. We con...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1994
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)90244-5