Convex partial transversals of planar regions

09/26/2018

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by   Vahideh Keikha, et al.

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We consider the problem of testing, for a given set of planar regions R and an integer k, whether there exists a convex shape whose boundary intersects at least k regions of R. We provide a polynomial time algorithm for the case where the regions are disjoint line segments with a constant number of orientations. On the other hand, we show that the problem is NP-hard when the regions are intersecting axis-aligned rectangles or 3-oriented line segments. For several natural intermediate classes of shapes (arbitrary disjoint segments, intersecting 2-oriented segments) the problem remains open.