Abstract
Given m unit disks and n points in the plane, the discrete unit disk cover problem is to select a minimum subset of the disks to cover the points. This problem is NP-hard [11] and the best previous practical solution is a 38-approximation algorithm by Carmi et al. [4]. We first consider the line-separable discrete unit disk cover problem (the set of disk centres can be separated from the set of points by a line) for which we present an O(m 2 n)-time algorithm that finds an exact solution. Combining our line-separable algorithm with techniques from the algorithm of Carmi et al. [4] results in an O(m 2 n 4) time 22-approximate solution to the discrete unit disk cover problem.
Funding for this project was provided by the NSERC Strategic Grant on Optimal Data Structures for Organization and Retrieval of Spatial Data.
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Claude, F., Dorrigiv, R., Durocher, S., Fraser, R., López-Ortiz, A., Salinger, A. (2009). Practical Discrete Unit Disk Cover Using an Exact Line-Separable Algorithm. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_7
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DOI: https://doi.org/10.1007/978-3-642-10631-6_7
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