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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. 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 number 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.
CitacióAloupis, G. [et al.]. Matching points with things. A: Latin American Theoretical Informatics Symposium. "9th Latin American Theoretical Informatics Symposium". Oaxaca: Springer Verlag, 2010, p. 456-467.