Graph-Theoretic Solutions to Computational Geometry Problems

Details Graph-Theoretic Solutions to Computational Geometry Problems Graph-Theoretic Solutions to Computational Geometry Problems

2009-08-26

arxiv.org/abs/0908.3916v1

Computer Science

Computational Geometry

16 pages, 7 figures

Scientific paper

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.

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