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The Annual International Conference on Geographic Information Science

GIScience 2016: Geographic Information Science pp 18–33Cite as

Partitioning Polygons via Graph Augmentation

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Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9927))

Abstract

We study graph augmentation under the dilation criterion. In our case, we consider a plane geometric graph \(G = (V,E)\) and a set C of edges. We aim to add to G a minimal number of nonintersecting edges from C to bound the ratio between the graph-based distance and the Euclidean distance for all pairs of vertices described by C. Motivated by the problem of decomposing a polygon into natural subregions, we present an optimal linear-time algorithm for the case that P is a simple polygon and C models an internal triangulation of P. The algorithm admits some straightforward extensions. Most importantly, in pseudopolynomial time, it can approximate a solution of minimum total length or, if C is weighted, compute a solution of minimum total weight. We show that minimizing the total length or the total weight is weakly NP-hard.

Finally, we show how our algorithm can be used for two well-known problems in GIS: generating variable-scale maps and area aggregation.

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Notes

  1. 1.

    In this paper “edge” always indicates an element of \(P \cup C\)—a node in \(\mathcal {T}\)—and never an edge between nodes (parent-child relation) in \(\mathcal {T}\).

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Acknowledgments

The authors would like to thank Johannes Oehrlein for helpful discussions on the topic of this paper. W. Meulemans is supported by Marie Skłodowska-Curie Action MSCA-H2020-IF-2014 656741.

Author information

Authors and Affiliations

  1. Institute of Computer Science, University of Osnabrück, Osnabrück, Germany

    Jan-Henrik Haunert

  2. giCentre, City University London, London, UK

    Wouter Meulemans

Authors
  1. Jan-Henrik Haunert
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  2. Wouter Meulemans
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Corresponding author

Correspondence to Jan-Henrik Haunert .

Editor information

Editors and Affiliations

  1. University of Texas at Austin , Austin, Texas, USA

    Jennifer A. Miller

  2. University of California at Berkeley , Berkeley, California, USA

    David O'Sullivan

  3. University of Wisconsin-Madison , Madison, Wisconsin, USA

    Nancy Wiegand

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Haunert, JH., Meulemans, W. (2016). Partitioning Polygons via Graph Augmentation. In: Miller, J., O'Sullivan, D., Wiegand, N. (eds) Geographic Information Science. GIScience 2016. Lecture Notes in Computer Science(), vol 9927. Springer, Cham. https://doi.org/10.1007/978-3-319-45738-3_2

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  • DOI: https://doi.org/10.1007/978-3-319-45738-3_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45737-6

  • Online ISBN: 978-3-319-45738-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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