A set of vertices D of a graph G is geodetic if every vertex of G lies on a shortest path between two not necessarily distinct vertices in D. The geodetic number of G is the minimu...
In this paper we investigate the relations between spanners, weak spanners, and power spanners in RD for any dimension D and apply our results to topology control in wireless netw...
Christian Schindelhauer, Klaus Volbert, Martin Zie...
In recent years, considerable advances have been made in the study of properties of metric spaces in terms of their doubling dimension. This line of research has not only enhanced...
For c ∈ R, a c-spanner is a subgraph of a complete Euclidean graph satisfying that between any two vertices there exists a path of weighted length at most c times their geometric...
Christian Schindelhauer, Klaus Volbert, Martin Zie...
During the last decade, incremental sampling-based motion planning algorithms, such as the Rapidly-exploring Random Trees (RRTs), have been shown to work well in practice and to po...