New results on stabbing segments with a polygon
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We consider a natural variation of the concept of stabbing a set of segments with a simple polygon: a segment s is stabbed by a simple polygon P if at least one endpoint of s is contained in P, and a segment set S is stabbed by P if P stabs every element of S. Given a segment set S, we study the problem of finding a simple polygon P stabbing S in a way that some measure of P (such as area or perimeter) is optimized. We show that if the elements of S are pairwise disjoint, the problem can be solved in polynomial time. In particular, this solves an open problem posed by Loftier and van Kreveld [Algorithmica 56(2), 236-269 (2010)]  about finding a maximum perimeter convex hull for a set of imprecise points modeled as line segments. Our algorithm can also be extended to work for a more general problem, in which instead of segments, the set S consists of a collection of point sets with pairwise disjoint convex hulls. We also prove that for general segments our stabbing problem is NP-hard. (C) 2014 Elsevier B.V. All rights reserved.
CitacióDíaz, J., Korman, M., Pérez, P., Pilz, A., Seara, C., Silveira, R.I. New results on stabbing segments with a polygon. "Computational geometry: theory and applications", 1 Gener 2015, vol. 48, núm. 1, p. 14-29.
Versió de l'editorhttp://www.sciencedirect.com/science/article/pii/S0925772114000686