We consider the classical problems (Edge) Steiner Tree and Vertex after restricting input to some class of graphs characterized by a small set forbidden induced subgraphs. show dichotomy for former problem restricted (H1,H2)-free latter H-free graphs. find that there exists an infinite family H such is polynomial-time solvable graphs, whereas exist only two which this holds Edge (assuming P≠NP)...

In a seminal paper, Chen, Roughgarden and Valiant [7] studied cost sharing protocols for network design with the objective to implement a low-cost Steiner forest as a Nash equilibrium of an induced cost-sharing game. One of the most intriguing open problems up to date is to understand the power of budget-balanced and separable cost sharing protocols in order to induce low-cost Steiner forests. ...

We consider low connectivity variants of the Survivable Network with Minimum Number of Steiner Points (SN-MSP) problem: given a finite set R of terminals in a metric space (M,d), a subset B ⊆ R of “unstable” terminals, and connectivity requirements {ruv : u, v ∈ R}, find a minimum size set S ⊆ M of additional points such that the unit-disc graph of R∪S contains ruv pairwise internally edge-disj...

mathematical chemistry is a branch of theoretical chemistry for discussion and prediction of the molecular structure using mathematical methods without necessarily referring to quantum mechanics. in theoretical chemistry, distance-based molecular structure descriptors are used for modeling physical, pharmacologic, biological and other properties of chemical compounds. the wiener polarity index ...

We address the problem of generating 2D quality triangle meshes from a set of constraints provided as a planar straight line graph. The algorithm first computes a constrained Delaunay triangulation of the input set of constraints, then interleaves Delaunay refinement and optimization. The refinement stage inserts a subset of the Voronoi vertices and midpoints of constrained edges as Steiner poi...

The chromatic number of a graph G, denoted by χ(G), is the minimum number of colors such that G can be colored with these colors in such a way that no two adjacent vertices have the same color. A clique in a graph is a set of mutually adjacent vertices. The maximum size of a clique in a graph G is called the clique number of G. The Turán graph Tn(k) is a complete k-partite graph whose partition...

We suggest a novel distance-based method for the determination of phylogenetic trees. It is based on multidimensional scaling and Euclidean Steiner trees in high-dimensional spaces. Preliminary computational experience shows that the use of Euclidean Steiner trees for finding phylogenetic trees is a viable approach. Experiments also indicate that the new method is comparable with results produc...

The Covering Steiner problem is a common generalization of the k-MST and Group Steiner problems. An instance of the Covering Steiner problem consists of an undirected graph with edge-costs, and some subsets of vertices called groups, with each group being equipped with a non-negative integer value (called its requirement); the problem is to find a minimum-cost tree which spans at least the requ...