Time delayed discounted Steiner trees to locate two or more discounted Steiner points

Approximations for Steiner Trees with Minimum Number of Steiner Points

Given n terminals in the Euclidean plane and a positive constant, find a Steiner tree interconnecting all terminals with the minimum number of Steiner points such that the Euclidean length of each edge is no more than the given positive constant. This problem is NP-hard with applications in VLSI design, WDM optical networks and wireless communications. In this paper, we show that (a) the Steine...

Steiner Trees and Steiner Forests

Two-level rectilinear Steiner trees

Given a set P of terminals in the plane and a partition of P into k subsets P1, . . . , Pk, a two-level rectilinear Steiner tree consists of a rectilinear Steiner tree Ti connecting the terminals in each set Pi (i = 1, . . . , k) and a top-level tree Ttop connecting the trees T1, . . . , Tk. The goal is to minimize the total length of all trees. This problem arises naturally in the design of lo...

Once More about 80 Steiner Triple Systems on 15 Points Once More about 80 Steiner Triple Systems on 15 Points

Subsets of a v-set are in one-to-one correspondence with vertices of a v-dimensional unit cube, a Delaunay polytope of the lattice Z v. All vertices of the same cardinality k generate a (v?1)-dimensional root lattice A v?1 and are vertices of the Delaunay polytope P(v; k) of the lattice A v?1. Hence k-blocks of a t ? (v; k;) design, being identiied with vertices of P(v; k), generate a sub-latti...

On the location of Steiner points in uniformly-oriented Steiner trees