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Steiner trees have been extensively studied in the context of weighted graphs. The prototype is, arguably, the Steiner tree problem in graphs. Let G = (V, E) be an undirected graph with non-negative edge weights c and let S ⊆ V be a subset of vertices, called terminals. A Steiner tree is a tree in G that spans S.
Minimum degree spanning tree; Minimum k-cut; Minimum k-spanning tree; Minor testing (checking whether an input graph contains an input graph as a minor); the same holds with topological minors; 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 ...
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 ...
"An Approximate Max-Steiner-Tree-Packing Min-Steiner-Cut Theorem" Marcin Mucha , Piotr Sankowski (Warsaw) "Maximum Matchings via Gaussian Elimination" 2003: Subhash Khot "Hardness of Approximating the Shortest Vector Problem in High Lp Norms" 2002: Boaz Barak
However, for this choice of k, it is possible for k-spanning tree to include only as few edges of the original graph as are needed to connect all the terminals. Therefore, the k-minimum spanning tree must be formed by combining the optimal Steiner tree with enough of the zero-weight edges of the added trees to make the total tree size large enough.
This bound is desirable in various applications, such as Steiner triple system. A Steiner Triple System is a 3-uniform, simple hypergraph in which every pair of vertices is contained in precisely one edge. Since a Steiner Triple System is clearly d=(n-1)/2-regular, the above bound supplies the following asymptotic improvement.
Despite the persistent rise in living costs due to inflation over the past two years, certain goods and services have become more affordable, offering a reprieve for consumers. While inflation has...
The single-trunk Steiner tree is a tree that consists of a single horizontal segment and some vertical segments. A minimum single-trunk Steiner tree (MSTST) may be found in O ( n log n ) time. However simply finding all its edges requires linear time .