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An exact algorithm for constructing minimum Euclidean skeletons of polygons

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Abstract

A Euclidean skeleton is a set of edges in the interior (or on the boundary) of a polygon that intersects any line segment that joins two points outside of the polygon and that intersects the polygon. In this paper we study minimum cardinality Euclidean skeletons and develop an algorithm for constructing them. We first prove a number of structural properties of minimum skeletons and use these to develop a canonical form. We then design an exact algorithm which initially generates a set of canonical skeleton edges, then executes a pruning module to reduce the set of candidate edges, and finally runs existing integer linear programming code to output an optimal solution. Finally, we perform computational testing on our algorithm to demonstrate its performance, and observe a number of experimental properties of minimum skeletons.

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Authors and Affiliations

  1. School of Mathematics and Statistics, The University of Melbourne, Melbourne, VIC, 3010, Australia

    Nicolau Andrés-Thió & Charl Ras

  2. School of Engineering, The University of Melbourne, Melbourne, VIC, 3010, Australia

    Marcus Brazil, Doreen Thomas & Marcus Volz

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  1. Nicolau Andrés-Thió
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  2. Marcus Brazil
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  3. Charl Ras
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  4. Doreen Thomas
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  5. Marcus Volz
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Correspondence to Charl Ras.

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Andrés-Thió, N., Brazil, M., Ras, C. et al. An exact algorithm for constructing minimum Euclidean skeletons of polygons. J Glob Optim 83, 137–162 (2022). https://doi.org/10.1007/s10898-021-01101-3

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  • DOI: https://doi.org/10.1007/s10898-021-01101-3

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