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A series of papers provided approximation algorithms for the minimum Steiner tree problem with approximation ratios that improved upon the 2 − 2/t ratio. This sequence culminated with Robins and Zelikovsky's algorithm in 2000 which improved the ratio to 1.55 by iteratively improving upon the minimum cost terminal spanning tree.
The RSMT is an NP-hard problem, and as with other NP-hard problems, common approaches to tackle it are approximate algorithms, heuristic algorithms, and separation of efficiently solvable special cases. An overview of the approaches to the problem may be found in the 1992 book by Hwang, Richards and Winter, The Steiner Tree Problem. [3]
Steiner tree, or Minimum spanning tree for a subset of the vertices of a graph. [2] (The minimum spanning tree for an entire graph is solvable in polynomial time.) Modularity maximization [5] Monochromatic triangle [3]: GT6 Pathwidth, [6] or, equivalently, interval thickness, and vertex separation number [7] Rank coloring; k-Chinese postman
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
Example of Steiner points (in red) added to a triangulation to improve the quality of triangles. In computational geometry , a Steiner point is a point that is not part of the input to a geometric optimization problem but is added during the solution of the problem, to create a better solution than would be possible from the original points alone.
Ding-Zhu Du (born May 21, 1948) is a Professor in the Department of Computer Science at The University of Texas at Dallas. [1] He is known for his research on the Euclidean minimum Steiner trees, [2] including an attempted proof of Gilbert–Pollak conjecture on the Steiner ratio, and the existence of a polynomial-time heuristic with a performance ratio bigger than the Steiner ratio.
The Steiner ratio is the supremum, over all point sets, of the ratio of lengths of the Euclidean minimum spanning tree to the Steiner minimum tree. Because the Steiner minimum tree is shorter, this ratio is always greater than one. [2] A lower bound on the Steiner ratio is provided by three points at the vertices of an equilateral triangle of ...
The optimal solutions to the Steiner tree problem and the minimum Wiener connector can differ. Define the set of query vertices Q by Q = {v 1, ..., v 10}.The unique optimal solution to the Steiner tree problem is Q itself, which has Wiener index 165, whereas the optimal solution for the minimum Wiener connector problem is Q ∪ {r 1, r 2}, which has Wiener index 142.