On the configuration space of Steiner minimal trees
نویسنده
چکیده
Among other results, we prove the following theorem about Steiner minimal trees in ddimensional Euclidean space: if two finite sets in R have unique and combinatorially equivalent Steiner minimal trees, then there is a homotopy between the two sets that maintains the uniqueness and the combinatorial structure of the Steiner minimal tree throughout the homotopy.
منابع مشابه
Bottleneck Distances and Steiner Trees in the Euclidean d-Space
Some of the most efficient heuristics for the Euclidean Steiner minimal trees in the d-dimensional space, d ≥ 2, use Delaunay tessellations and minimum spanning trees to determine small subsets of geometrically close terminals. Their low-cost Steiner trees are determined and concatenated in a greedy fashion to obtain low cost trees spanning all terminals. The weakness of this approach is that o...
متن کاملA faster dynamic programming algorithm for exact rectilinear Steiner minimal trees
An exact rectilinear Steiner minimal tree algorithm is presented that improves upon the time and space complexity of previous guarantees and is easy to implement. Experimental evidence is presented that demonstrates that the algorithm also works well an practice.
متن کاملQuantitative Illumination of Convex Bodies and Vertex Degrees of Geometric Steiner Minimal Trees
In this note we prove two results on the quantitative illumination parameter f (d) of the unit ball of a d-dimensional normed space introduced by K. Bezdek (1992). The first is that f (d) = O(2dd2 log d). The second involves Steiner minimal trees. Let v(d) be the maximum degree of a vertex, and s(d) of a Steiner point, in a Steiner minimal tree in a d-dimensional normed space, where both maxima...
متن کاملSteiner Minimal Trees in Simple Polygons
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 کاملComputing Steiner minimal trees in Euclidean d-space
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013