Abstract
Let \(\mathcal R\) be a set of n colored imprecise points, where each point is colored by one of k colors. Each imprecise point is specified by a unit disk in which the point lies. We study the problem of computing the smallest and the largest possible minimum color spanning circle, among all possible choices of points inside their corresponding disks. We present an \(O(nk\log n)\) time algorithm to compute a smallest minimum color spanning circle. Regarding the largest minimum color spanning circle, we show that the problem is \(\mathsf {NP}\text {-}\mathsf {Hard}\) and present a \(\frac{1}{3}\)-factor approximation algorithm. We improve the approximation factor to \(\frac{1}{2}\) for the case where no two disks of distinct color intersect.
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Acknowledgements
The authors would like to thank Irina Kostitsyna for key discussions on the hardness reduction and Hans Raj Tiwary for the proof of Lemma 5. A.A., R.J., V.K., and M. S. were supported by the Czech Science Foundation, grant number GJ19-06792Y, and by institutional support RVO: 67985807. M.L. was partially supported by the Netherlands Organization for Scientific Research (NWO) under project no. 614.001.504. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 734922.
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Acharyya, A., Jallu, R.K., Keikha, V., Löffler, M., Saumell, M. (2021). Minimum Color Spanning Circle in Imprecise Setup. In: Chen, CY., Hon, WK., Hung, LJ., Lee, CW. (eds) Computing and Combinatorics. COCOON 2021. Lecture Notes in Computer Science(), vol 13025. Springer, Cham. https://doi.org/10.1007/978-3-030-89543-3_22
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