Abstract
A point-setS is protecting a collection F =T 1,T 2,..., n ofn mutually disjoint compact sets if each one of the setsT i is visible from at least one point inS; thus, for every setT i ∈F there are points xS andy T i such that the line segment joining x to y does not intersect any element inF other thanT i . In this paper we prove that [2(n-2)/3] points are always sufficient and occasionally necessary to protect any family F ofn mutually disjoint compact convex sets. For an isothetic family F, consisting ofn mutually disjoint rectangles, [n/2] points are always sufficient and [n/2] points are sometimes necessary to protect it. IfF is a family of triangles, [4n/7] points are always sufficient. To protect families ofn homothetic triangles, [n/2] points are always sufficient and [n/2] points are sometimes necessary.
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This research was supported by the Natural Sciences and Engineering Research Council of Canada, grant numbers OGP0000977 and OGP0023992.
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Czyzowicz, J., Rivera-Campo, E., Urrutia, J. et al. Protecting convex sets. Graphs and Combinatorics 10, 311–321 (1994). https://doi.org/10.1007/BF02986681
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DOI: https://doi.org/10.1007/BF02986681