LIPIcs.SoCG.2017.4.pdf
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Minimum Perimeter-Sum Partitions in the Plane
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33rd International Symposium on Computational Geometry (SoCG 2017)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Computational Geometry (SoCG) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2017-06-20
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Mikkel Abrahamsen, Mark de Berg, Kevin Buchin, Mehran Mehr, and Ali D. Mehrabi. Minimum Perimeter-Sum Partitions in the Plane. In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 4:1-4:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.SoCG.2017.4
https://doi.org/10.4230/LIPIcs.SoCG.2017.4
Abstract
Let P be a set of n points in the plane. We consider the problem of partitioning P into two subsets P_1 and P_2 such that the sum of the perimeters of CH(P_1) and CH(P_2) is minimized, where CH(P_i) denotes the convex hull of P_i. The problem was first studied by Mitchell and Wynters in 1991 who gave an O(n^2) time algorithm. Despite considerable progress on related problems, no subquadratic time algorithm for this problem was found so far. We present an exact algorithm solving the problem in O(n log^4 n) time and a (1+e)-approximation algorithm running in O(n + 1/e^2 log^4(1/e)) time.
Keywords
- Computational geometry
- clustering
- minimum-perimeter partition
- convex hull
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