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• W2122986136 abstract "Given an ordered set of points and an ordered set of geometric objects in the plane, we are interested in finding a non-crossing matching between point–object pairs. In this paper, we address the algorithmic problem of determining whether a non-crossing matching exists between a given point–object pair. We show that when the objects we match the points to are finite point sets, the problem is NP-complete in general, and polynomial when the objects are on a line or when their size is at most 2. When the objects are line segments, we show that the problem is NP-complete in general, and polynomial when the segments form a convex polygon or are all on a line. Finally, for objects that are straight lines, we show that the problem of finding a min-max non-crossing matching is NP-complete." @default.
• W2122986136 created "2016-06-24" @default.
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• W2122986136 date "2013-01-01" @default.
• W2122986136 modified "2023-09-27" @default.
• W2122986136 title "Non-crossing matchings of points with geometric objects" @default.
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• W2122986136 doi "https://doi.org/10.1016/j.comgeo.2012.04.005" @default.
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