Geometric Multicut: Shortest Fences for Separating Groups of Objects in the Plane
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- OA-Geometric Multicut - Shortest Fences for Separating Groups
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We study the following separation problem: Given a collection of pairwise disjoint coloured objects in the plane with k different colours, compute a shortest “fence” F, i.e., a union of curves of minimum total length, that separates every pair of objects of different colours. 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, as it is a geometric analog to the well-studied multicut problem on graphs. We first give an O(n4log3n)-time algorithm that computes an optimal fence for the case where the input consists of polygons of two colours with n corners in total. We then show that the problem is NP-hard for the case of three colours. Finally, we give a randomised 4/3⋅1.2965-approximation algorithm for polygons and any number of colours.
Original language | English |
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Journal | Discrete & Computational Geometry |
Volume | 64 |
Pages (from-to) | 575–607 |
ISSN | 0179-5376 |
DOIs | |
Publication status | Published - 2020 |
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