The Steiner tree problem requires a shortest tree spanning a given vertex subset S within graph G = @‘, El. Two heuristics finding approximate Steiner trees no longer than 11/6 times of the optima1 length appeared recently. They run in time O(CY + KS2 + S4) and O(a + l@ + S3s), respectively, where LY is the time complexity of the all-pairs-shortest-paths problem. We reduce the runtime of the fi...

The geometric bottleneck Steiner network problem on a set of vertices X embedded in a normed plane requires one to construct a graph G spanning X and a variable set of k ≥ 0 additional points, such that the length of the longest edge is minimised. If no other constraints are placed on G then a solution always exists which is a tree. In this paper we consider the Eu-clidean bottleneck Steiner ne...

Generalized Steiner systems GSd…t; k; v; g† were ®rst introduced by Etzion and used to construct optimal constant-weight codes over an alphabet of size g‡ 1 with minimum Hamming distance d, in which each codeword has length v and weight k. Much work has been done for the existence of generalized Steiner triple systems GS…2; 3; v; g†. However, for block size four there is not much known on GSd…2...

The novel octilinear routing paradigm (X-architecture) in VLSI design requires new approaches for the construction of Steiner trees. In this paper, we consider two versions of the shortest octilinear Steiner tree problem for a given point set K of terminals in the plane: (1) a version in the presence of hard octilinear obstacles, and (2) a version with rectangular soft obstacles. The interior o...

The geometric bottleneck Steiner network problem on a set of vertices X embedded in a normed plane requires one to construct a graph G spanning X and a variable set of k ≥ 0 additional points, such that the length of the longest edge is minimised. If no other constraints are placed on G then a solution always exists which is a tree. In this paper we consider the Eu-clidean bottleneck Steiner ne...

As we move to deep sub-micron designs below 0.18 microns, the delay of a circuit, as well as power dissipation and area, is dominated by interconnections between logical elements (i.e. transistors)[1]. The focus of this paper is on the global routing problem. Both global and channel routing are NP-hard[2]; therefore, all existing solution methodologies are heuristics. The main aim is to develop...

If A and K are compact convex sets in Rn, a Steiner-type formula is valid for the erosion of A by K if and only if A is open with respect to K. The if part is proved in the general case. The only if part is conjectured, and proved only in the case n = 2.

The problem we consider in this article is motivated by data placement in particular data replication in video on demand systems. We are given a set V of n servers and b files (data, documents). Each file is replicated on exactly k servers. The problem is to determine the placement that minimizes the variance of the number of unavailable datas. To do that, we consider the problem of determining...

Given an undirected hypergraph and a subset of vertices S ⊆ V with a specified root vertex r ∈ S, the Steiner Rooted-Orientation problem is to find an orientation of all the hyperedges so that in the resulting directed hypergraph the “connectivity” from the root r to the vertices in S is maximized. This is motivated by a multicasting problem in undirected networks as well as a generalization of...

A Steiner triple system of order v (briefly STS(v)) is a pair (X, B) where X is a v-set and B is a collection of 3-subset of X (called triple) such that every pair of distinct elements of X belongs to exactly one triple of B. A Kirkman triple system of order v (briefly KTS(v)) is a Steiner triple system of order v (X, B) together with a partition R of the set of triples B into subsets R1 , R2 ,...