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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.
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
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]
In combinatorial optimization, the minimum Wiener connector problem is the problem of finding the minimum Wiener connector. It can be thought of as a version of the classic Steiner tree problem (one of Karp's 21 NP-complete problems), where instead of minimizing the size of the tree, the objective is to minimize the distances in the subgraph ...
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.
[7] Its 11 chapters cover quantitative geometry, a history of computational geometry, mesh generation, automated generation of geometric proofs, randomized geometric algorithms, Steiner tree problems, Voronoi diagrams and Delaunay triangulations, constraint solving, spline surfaces, network design, and numerical primitives for geometric computing.
If the input points alone are used as endpoints of the network edges, then the shortest network is their minimum spanning tree. However, shorter networks can often be obtained by adding Steiner points, and using both the new points and the input points as edge endpoints. [1] Another problem that uses Steiner points is Steiner triangulation. The ...
In computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete.In his 1972 paper, "Reducibility Among Combinatorial Problems", [1] Richard Karp used Stephen Cook's 1971 theorem that the boolean satisfiability problem is NP-complete [2] (also called the Cook-Levin theorem) to show that there is a polynomial time many-one reduction ...