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Covering Part of a Planar Network

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Abstract

The problem of locating facilities in a feasible area covering some parts of network links within a given radius is analyzed. The feasible area can be the interior (convex hull of the nodes) of a planar network or any union of convex polygons. Both minimization and maximization of coverage are considered. The single facility location problem is solved by the global optimization approach “Big Triangle Small Triangle.” The multiple facility maximization problem is solved by a specially designed heuristic algorithm. The idea of the heuristic algorithm may prove to work well on other planar multiple facility location problems. Computational experience with problems of up to 40,000 links demonstrate the effectiveness of the single facility and multiple facilities algorithms. The largest single facility minimal cover problem is solved in about one minute and the largest single facility maximal cover problem is solved in less than 4 minutes.

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Notes

  1. The code is available by email from the first author.

  2. We thank Atsuo Suzuki for providing and modifying the triangulation Fortran program.

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Acknowledgments

This research was supported, in part, by the Natural Sciences and Engineering Research Council of Canada.

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Authors and Affiliations

  1. Steven G. Mihaylo College of Business and Economics, California State University-Fullerton, Fullerton, CA, 92834, USA

    Zvi Drezner

  2. Faculty of Business McMaster University, Hamilton, Ont., L8S 4M4, Canada

    George O. Wesolowsky

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  1. Zvi Drezner
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  2. George O. Wesolowsky
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Correspondence to Zvi Drezner.

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Drezner, Z., Wesolowsky, G.O. Covering Part of a Planar Network. Netw Spat Econ 14, 629–646 (2014). https://doi.org/10.1007/s11067-014-9263-5

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