Abstract
Let P be a simple polygon, and let Q be a set of points in P. We present an almost-linear time algorithm for computing a minimum cover of Q by disks that are contained in P. We generalize the algorithm above, so that it can compute a minimum cover of Q by homothets of any fixed compact convex set \(\mathcal{O}\) of constant description complexity that are contained in P. This improves previous results of Katz and Morgenstern [20]. We also consider the disk-cover problem when Q is contained in a (not too wide) annulus, and present a nearly linear algorithm for this case too.
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Kaplan, H., Katz, M.J., Morgenstern, G., Sharir, M. (2010). Optimal Cover of Points by Disks in a Simple Polygon. In: de Berg, M., Meyer, U. (eds) Algorithms – ESA 2010. ESA 2010. Lecture Notes in Computer Science, vol 6346. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15775-2_41
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DOI: https://doi.org/10.1007/978-3-642-15775-2_41
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