Abstract
In this paper, we review and analyze the complexity of a paradigm called grouping-and-querying which has been used in the past for computing convex hulls of points or objects on the plane, maximal and convex layer decompositions, lower envelopes of functions, etc. Then, we present new results concerning the computation of: (i) a transversal set for various families of geometric objects, (ii) a few (not necessarily connected) cells of a Voronoi diagram: Let \(\mathcal{S}\) be a set of n points of the Euclidean plane \(\mathbb{E}^2\), we give an O(n log h) time algorithm for computing the Voronoi cells of the sites \(\mathcal{S}'\subseteq\mathcal{S}\), where h is the output-size. We extend this approach to higher dimensions.
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Nielsen, F. (2000). Grouping and Querying: A Paradigm to Get Output-Sensitive Algorithms. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 1998. Lecture Notes in Computer Science, vol 1763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-46515-7_21
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DOI: https://doi.org/10.1007/978-3-540-46515-7_21
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