eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-07-04
9:1
9:15
10.4230/LIPIcs.ICALP.2019.9
article
Geometric Multicut
Abrahamsen, Mikkel
1
https://orcid.org/0000-0003-2734-4690
Giannopoulos, Panos
2
Löffler, Maarten
3
Rote, Günter
4
https://orcid.org/0000-0002-0351-5945
BARC, University of Copenhagen, Universitetsparken 1, DK-2100 Copenhagen, Denmark
giCenter, Department of Computer Science, City University of London, EC1V 0HB, London, UK
Department of Information and Computing Sciences, Utrecht University, The Netherlands
Institut für Informatik, Freie Universität Berlin, Takustraße 9, 14195 Berlin, Germany
We study the following separation problem: Given a collection of colored objects in the plane, compute a shortest "fence" F, i.e., a union of curves of minimum total length, that separates every two objects of different colors. Two objects are separated if F contains a simple closed curve that has one object in the interior and the other in the exterior. We refer to the problem as GEOMETRIC k-CUT, where k is the number of different colors, as it can be seen as a geometric analogue to the well-studied multicut problem on graphs. We first give an O(n^4 log^3 n)-time algorithm that computes an optimal fence for the case where the input consists of polygons of two colors and n corners in total. We then show that the problem is NP-hard for the case of three colors. Finally, we give a (2-4/3k)-approximation algorithm.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol132-icalp2019/LIPIcs.ICALP.2019.9/LIPIcs.ICALP.2019.9.pdf
multicut
clustering
Steiner tree