Graph-Theoretic Solutions to Computational Geometry Problems

  • David Eppstein
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5911)


Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm depends on the special properties of the graph constructed in this way. We survey the art gallery problem, partition into rectangles, minimum-diameter clustering, rectilinear cartogram construction, mesh stripification, angle optimization in tilings, and metric embedding from this perspective.


Bipartite Graph Maximum Clique Simple Polygon Unit Disk Graph Auxiliary Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • David Eppstein
    • 1
  1. 1.Computer Science DepartmentUniversity of CaliforniaIrvine

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