By Daya Gaur, N.S. Narayanaswamy
This booklet constitutes the lawsuits of the 3rd overseas convention on Algorithms and Discrete utilized arithmetic, CALDAM 2017, held in Goa, India, in February 2017.
The 32 papers awarded during this quantity have been rigorously reviewed and chosen from 103 submissions. They take care of the subsequent components: algorithms, graph idea, codes, polyhedral combinatorics, computational geometry, and discrete geometry.
Read Online or Download Algorithms and Discrete Applied Mathematics: Third International Conference, CALDAM 2017, Sancoale, Goa, India, February 16-18, 2017, Proceedings PDF
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Additional info for Algorithms and Discrete Applied Mathematics: Third International Conference, CALDAM 2017, Sancoale, Goa, India, February 16-18, 2017, Proceedings
First, we study the combinatorial complexity of the nearest-site Voronoi diagram NVDP (S ) with respect to DP , where P is an m-sided convex polygon. We use the abstract Voronoi diagram paradigm of Klein and Wood . 6]. If DP satisﬁes Property 1, Property 3, and Property 4, then all Voronoi regions are simply connected. As a result, we have the following. Lemma 3. Every Voronoi region N VP (si ) in N V DP (S ) is simply connected. Let s1 , s2 be two line segments in the plane, and B(s1 , s2 ) and BP (s1 , s2 ) be the bisectors of s1 and s2 with respect to the Euclidean distance and the polygon-oﬀset distance DP , respectively.
The ﬁrst one is the largest empty rectangle problem (LER) where given a point set P , the goal is to ﬁnd a rectangle of the maximum area which does not contain any point of P in its interior [1,14,15,28,29]. This problem can be solved in O(|P |3 ) time with O(|P |2 ) space . The second problem is a bichromatic problem, where the goal is to ﬁnd the rectangle that contains all the red points, the minimum number of blue points and has the largest area. This problem can be solved in O(m3 + n log n) time .
On the complexity of higher order abstract Voronoi diagrams. Comput. Geom. Theory Appl. 48(8), 539–551 (2015) 5. : Farthest-polygon Voronoi diagrams. Comput. Geom. Theory Appl. 44(4), 234–247 (2011) 6. : Voronoi diagrams based on convex distance functions. In: O’Rourke, J. ) Proceedings of the First Annual Symposium on Computational Geometry, Baltimore, Maryland, USA, 5–7 June 1985, pp. 235–244. ACM (1985) 7. : Principia Philosophiae. Ludovicus Elzevirius, Amsterdam (1644) 8. : A sweepline algorithm for Voronoi diagrams.