We consider the robot exploration of a planar graphlike world. The robot's goal is to build a complete map of its environment. The environment is modeled as an arbitrary undi...
Ioannis M. Rekleitis, Vida Dujmovic, Gregory Dudek
We show that the number of vertices of a given degree k in several kinds of series-parallel labelled graphs of size n satisfy a central limit theorem with mean and variance proport...
Embedding metrics into constant-dimensional geometric spaces, such as the Euclidean plane, is relatively poorly understood. Motivated by applications in visualization, ad-hoc netw...
MohammadHossein Bateni, Mohammad Taghi Hajiaghayi,...
We address in this paper the problem of constructing embeddings of planar graphs satisfying declarative, user-defined topological constraints. The constraints consist each of a cy...
In this paper we construct two distributed algorithms for computing approximations of a largest matching and a minimum dominating set in planar graphs on n vertices. The approximat...
Andrzej Czygrinow, Michal Hanckowiak, Edyta Szyman...