Abstract
We consider the p-piercing problem for axis-parallel rectangles. We are given a collection of axis-parallel rectangles in the plane, and wish to determine whether there exists a set of p points whose union intersects all the given rectangles. We present efficient algorithms for finding a piercing set (i.e., a set of p points as above) for values of p = 1, 2, 3, 4, 5. The result for 4 and 5-piercing improves an existing result of O(n log3 n) and O(n log4 n) to O(n log n) time, and is applied to find a better rectilinear 5-center algorithm. We improve the existing algorithm for general (but fixed) p, and we also extend our algorithms to higher dimensional space. We also consider the problem of piercing a set of rectangular rings.
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© 1997 Springer-Verlag Berlin Heidelberg
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Segal, M. (1997). On piercing sets of axis-parallel rectangles and rings. In: Burkard, R., Woeginger, G. (eds) Algorithms — ESA '97. ESA 1997. Lecture Notes in Computer Science, vol 1284. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63397-9_33
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DOI: https://doi.org/10.1007/3-540-63397-9_33
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