A-Tree is a rectilinear Steiner tree in which every sink is connected to a driver by a shortest length path, while simultaneously minimizing total wire length. This paper presents a polynomial approximation algorithm for the generalized version of A-Tree problem with upper-bounded delays along each path from the driver to the sinks and with restrictions on the number of Steiner nodes. We refer ...

A Steiner System, denoted S(t, k, v), is a vertex set X containing v vertices, and a collection of subsets of X of size k, called blocks, such that every t vertices from X are in exactly one of the blocks. A Steiner Triple System, or STS, is a special case of a Steiner System where t = 2, k = 3 and v = 1 or 3 (mod6) [7]. A Bi-Steiner Triple System, or BSTS, is a Steiner Triple System with the v...

We show that any PSLG with v vertices can be tri angulated with no angle larger than by adding O v log v Steiner points in O v log v time We rst triangulate the PSLG with an arbitrary con strained triangulation and then re ne that triangula tion by adding additional vertices and edges We fol low a lazy strategy of starting from an obtuse angle and exploring the triangulation in search of a sequ...

A q-analog of a Steiner system (briefly, q-Steiner system), denoted by S = Sq[t, k, n], is a set of k-dimensional subspaces of F n q such that each t-dimensional subspace of Fq is contained in exactly one element of S. Presently, q-Steiner systems are known only for t = 1 and in the trivial cases t = k and k = n. In this paper, the first known nontrivial q-Steiner systems with t ≥ 2 are constru...

The Steiner tree problem is to nd the tree with minimal Euclidean length spanning a set of xed points in the plane, given the ability to add points (Steiner points). The problem is NP-hard, so polynomial-time heuristics are desired. We present two such heuristics, both of which utilize an eecient method for computing a locally optimal tree with a given topology. The rst systematically inserts S...

The Steiner tree problem asks for a shortest subgraph connecting a given set of terminals in a graph. It is known to be APX-complete, which means that no polynomial time approximation scheme can exist for this problem, unless P=NP. Currently, the best approximation algorithm for the Steiner tree problem has a performance ratio of + , , whereas the corresponding lower bound is smaller than + , ....

We are interested in what sizes of cliques are to be found in any arbitrary spanning graph of a Steiner triple system S. In this paper we investigate spanning graphs of projective Steiner triple systems, proving, not surprisingly, that for any positive integer k and any sufficiently large projective Steiner triple system S, every spanning graph of S contains a clique of size k.

Anthroposophy is a school of thought or esoteric philosophy that goes back to Rudolf Steiner. Steiner wanted to expand the human mind through imagination, inspiration, and intuition. His own insights originated mainly from the “Akasha-Chronicle.” This is the “nontransitory history that is not perceptible to the senses,” which apparently only Steiner could access. Steiner applied his concepts in...

The global routing problem decomposes the large, complex routing problem into a set of more manageable subproblems. The high correlation between the output of the global router and the detailed router enables the designer to efficiently use the global route to refine the design quickly before running the full detailed route. Hence, routability of the global routing solution is the key factor. T...

Many multicast routing algorithms have been suggested in the past as multicast communication emerges as one of the important services in communications networks. Many algorithms aim at the Steiner tree model because the Steiner tree is thought to provide the optimal multicast route by minimizing the sum of the link costs. The concept of cost in network routing can apply to various measures of n...