We combine Steiner systems with Hadamard matrices to produce a new class of equiangular tight frames. This in turn leads to new constructions of strongly regular graphs and distance-regular antipodal covers of the complete graph.

The total Steiner k-distance and the k-th total path length are the sum of the size of Steiner trees and ancestor-trees over sets of k nodes of a given tree, respectively. They are useful statistics with many applications. Consequently, they have been analyzed for many different random trees, including increasing tree, binary search tree, generalized m-ary search tree and simply generated trees...

Given a finite configuration of points in a metric space, a Steiner center (respectively, a centroid) is the point of the space (respectively, of the configuration) that minimizes the sum of the distances from all its elements. Working on the k-dimensional real space endowed with the Manhattan distance, we study the approximate algorithm that takes a point of minimum distance from the Steiner c...

Given a set P of n points with their pairwise distances, the traveling salesman problem (TSP) asks for a shortest tour that visits each point exactly once. We consider the rectilinear instances of the TSP, i.e. TSP instances where the points lie in the plane and the distance between two points is the l1 distance. We propose a fixed-parameter algorithm for the Rectilinear TSP running in O ( nh7 ...

Generalized Steiner points and the corresponding selections for setvalued maps share interesting commutation properties with set operations which make them suitable for the set-valued numerical problems presented here. This short overview will present first applications of these selections to standard problems in this area, namely representation of convex, compact sets in R and set operations, ...

Generalized Steiner systems GS (3, 4, v, 2) were first discussed by Etzion and used to construct optimal constant weight codes over an alphabet of size three with minimum Hamming distance three, in which each codeword has length v and weight four. Not much is known for GS (3, 4, v, 2)s except for a recursive construction and two small designs for v = 8, 10 given by Etzion. In this paper, more s...

In this paper we present a method for navigating a multirobot system through an environment while additionally maintaining a set of constraints. Our approach is based on graph structures that model movements and constraints separately, in order to cover different robots and a large class of possible constraints. Additionally, the partition of movement and constraint graph allows us to use known...

The minimum feature size of a planar straight-line graph is the minimum distance between a vertex and a nonincident edge. When a polygon is partitioned into a mesh, the degradation is the ratio of original to final minimum feature size. We show that some planar straight-line graphs cannot be triangulated with constant degradation, even with an unbounded number of Steiner points and triangles. T...

Given a connected graph G = (V, E) with non-negative edge costs, and a set of " special " nodes S ⊂ V , a subgraph of G is a Steiner tree, if it is a tree that spans (connects) all the (" special ") nodes in S. The Steiner Tree problem is to find a Steiner Tree of minimum weight (cost). Steiner Tree is an important NP-hard problem that is often encountered in practice. Examples include design o...