Geometric Multicut: Shortest Fences for Separating Groups of Objects in the Plane

Mikkel Abrahamsen, Panos Giannopoulos, Maarten Löffler, Günter Rote

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3 Citationer (Scopus)
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Abstract

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.
OriginalsprogEngelsk
TidsskriftDiscrete & Computational Geometry
Vol/bind64
Sider (fra-til)575–607
ISSN0179-5376
DOI
StatusUdgivet - 2020

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