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The Most Points Connected-Covering Problem with Two Disks

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Abstract

Let P be a set of points in the plane. The goal is to place two unit disks in the plane such that the number of points from P covered by the disks is maximized. In addition, the distance between the centers of the two disks should not exceed a specified constant Rc ≥ 0. We propose two algorithms to solve this problem. The first algorithm is a simple exhaustive algorithm which runs in O(n4) time. We then improve this algorithm by a constructing connectivity region and building a segment tree to compute two optimal disks. The resulting algorithm has \(O(n^{3} \log n)\) time complexity.

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Notes

  1. For the cases that the graph is not connected, it can be connected by adding some extra edges between connected sub-graphs.

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Acknowledgements

This research was in part supported by a grant from IPM. (No. CS1397-4-64).

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Authors and Affiliations

  1. SSRD Lab, Department of Computer Engineering and Information Technology, Amirkabir University of Technology, 424 Hafez Ave., Tehran, Iran

    Sanaz Soltani & Mohammadreza Razzazi

  2. Department of Computer Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

    Hossein Ghasemalizadeh

  3. School of Computer Science, Institute for Research in Fundamental Sciences(IPM), P.O. Box:19395-5746, Tehran, Iran

    Mohammadreza Razzazi

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  1. Sanaz Soltani
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  2. Mohammadreza Razzazi
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Correspondence to Sanaz Soltani.

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Soltani, S., Razzazi, M. & Ghasemalizadeh, H. The Most Points Connected-Covering Problem with Two Disks. Theory Comput Syst 62, 2035–2047 (2018). https://doi.org/10.1007/s00224-018-9870-5

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  • DOI: https://doi.org/10.1007/s00224-018-9870-5

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