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- W3037475288 abstract "We study the following separation problem: Given a collection of colored objects in the plane, compute a shortest $F$, 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 $O(n^4log^3 n)$-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." @default.
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- W3037475288 date "2019-02-11" @default.
- W3037475288 modified "2023-09-27" @default.
- W3037475288 title "Geometric Multicut" @default.
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