Abstract
We describe and analyze the first adaptive algorithm for merging k convex hulls in the plane. This merging algorithm in turn yields a synergistic algorithm to compute the convex hull of a set of planar points, taking advantage both of the positions of the points and their order in the input. This synergistic algorithm asymptotically outperforms all previous solutions for computing the convex hull in the plane.
C. Ochoa is supported by CONICYT-PCHA/Doctorado Nacional/2013-63130161 (Chile).
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Notes
- 1.
A dovetailing combination of k algorithms executes the k algorithms in parallel and stops as soon as one of the algorithms finishes.
- 2.
Doubling search is a technique for searching sorted unbounded arrays in which an element of rank k is found by performing \(2\log {k}\) comparisons [4].
- 3.
Even though the Steps 2 and 3 do not discard or output blocks of points by themselves we include them in the same analysis as the Steps 4 and 6.
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Barbay, J., Ochoa, C. (2018). Synergistic Solutions for Merging and Computing Planar Convex Hulls. In: Wang, L., Zhu, D. (eds) Computing and Combinatorics. COCOON 2018. Lecture Notes in Computer Science(), vol 10976. Springer, Cham. https://doi.org/10.1007/978-3-319-94776-1_14
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