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M. Nöllenburg, R. Prutkin, I. Rutter:
"Partitioning Graph Drawings and Triangulated Simple Polygons into Greedily Routable Regions";
International Journal of Computational Geometry & Applications, 27 (2017), 1+2; S. 121 - 158.

A greedily routable region (GRR) is a closed subset of R^2, in which any destination point can be reached from any starting point by always moving in the direction with maximum reduction of the distance to the destination in each point of the path. Recently, Tan and Kermarrec proposed a geographic routing protocol for dense wireless sensor networks based on decomposing the network area into a small number of interior-disjoint GRRs. They showed that minimum decomposition is NP-hard for polygonal regions with holes. We consider minimum GRR decomposition for plane straight-line drawings of graphs. Here, GRRs coincide with self-approaching drawings of trees, a drawing style which has become a popular research topic in graph drawing. We show that minimum decomposition is still NP-hard for graphs with cycles and even for trees, but can be solved optimally for trees in polynomial time, if we allow only certain types of GRR contacts. Additionally, we give a 2-approximation for simple polygons, if a given triangulation has to be respected.

Greedy region decomposition; increasing-chord drawings; decomposing graph drawings; greedy routing in wireless sensor networks Read More: http://www.worldscientific.com/doi/abs/10.1142/S0218195917600068

http://dx.doi.org/10.1142/S0218195917600068

http://www.worldscientific.com/doi/abs/10.1142/S0218195917600068