eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-06-20
4:1
4:15
10.4230/LIPIcs.SoCG.2017.4
article
Minimum Perimeter-Sum Partitions in the Plane
Abrahamsen, Mikkel
de Berg, Mark
Buchin, Kevin
Mehr, Mehran
Mehrabi, Ali D.
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol077-socg2017/LIPIcs.SoCG.2017.4/LIPIcs.SoCG.2017.4.pdf
Computational geometry
clustering
minimum-perimeter partition
convex hull