Abstract
Let X be a simple region (e.g., a simple polygon), and let Q be a set of points in X. Let O be a convex object, such as a disk, a square, or an equilateral triangle. We present a scheme for computing a minimum cover of Q, consisting of homothets of O contained in X. In particular, a minimum disk cover of Q with respect to X, can be computed in polynomial time.
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A preliminary version of this paper has appeared in the 11th Algorithms and Data Structures Symposium, WADS 2009.
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Katz, M.J., Morgenstern, G. A Scheme for Computing Minimum Covers within Simple Regions. Algorithmica 62, 349–360 (2012). https://doi.org/10.1007/s00453-010-9458-1
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DOI: https://doi.org/10.1007/s00453-010-9458-1