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Connecting red cells in a bicolour Voronoi diagram. (English) Zbl 1374.68624
Márquez, Alberto (ed.) et al., Computational geometry. XIV Spanish meeting on computational geometry, EGC 2011, dedicated to Ferran Hurtado on the occasion of his 60th birthday, Alcalá de Henares, Spain, June 27–30, 2011. Revised selected papers. Berlin: Springer (ISBN 978-3-642-34190-8/pbk). Lecture Notes in Computer Science 7579, 210-219 (2012).
Summary: Let \(S\) be a set of \(n + m\) sites, of which \(n\) are red and have weight \(w _{R }\), and \(m\) are blue and weigh \(w_{B }\). The objective of this paper is to calculate the minimum value of the red sites’ weight such that the union of the red Voronoi cells in the weighted Voronoi diagram of \(S\) is a connected region. This problem is solved for the multiplicatively-weighted Voronoi diagram in \(\mathcal{O}((n+m)^2 \log (nm))\) time and for both the additively-weighted and power Voronoi diagram in \(\mathcal{O}(nm \log (nm))\) time.
For the entire collection see [Zbl 1253.68016].
MSC:
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
68Q25 Analysis of algorithms and problem complexity
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