Partitioning Graph Drawings and Triangulated Simple Polygons into Greedily Routable Regions

  • Martin Nöllenburg
  • Roman Prutkin
  • Ignaz Rutter
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9472)


A greedily routable region (GRR) is a closed subset of \(\mathbb R^2\), in which each destination point can be reached from each starting point by choosing 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 polygons 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, but can be solved optimally for trees in polynomial time. Additionally, we give a 2-approximation for simple polygons, if a given triangulation has to be respected.



The second author thanks Jie Gao for pointing him to the topic of GRR decompositions.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Martin Nöllenburg
    • 1
  • Roman Prutkin
    • 2
  • Ignaz Rutter
    • 2
  1. 1.Algorithms and Complexity GroupTU WienViennaAustria
  2. 2.Institute of Theoretical InformaticsKarlsruhe Institute of TechnologyKarlsruheGermany

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