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2008
Springer

The Parameterized Complexity of the Rectangle Stabbing Problem and Its Variants

8 years 4 months ago
The Parameterized Complexity of the Rectangle Stabbing Problem and Its Variants
We study the parameterized complexity of an NP-complete geometric covering problem called d-dimensional Rectangle Stabbing where we are given a set of axis-parallel d-dimensional hyperrectangles, a set of axis-parallel (d- 1)-dimensional hyperplanes and a positive integer k; the question is whether one can select at most k hyperplanes so that every hyperrectangle is intersected by at least one of them. This problem is well-studied from the approximation point of view, while its parameterized complexity remained unexplored so far. We show that the case d 3 is W[1]-hard with respect to the parameter k. The case d = 2 is still open and we investigate several natural restrictions of this case and show them to be fixed-parameter tractable.
Michael Dom, Somnath Sikdar
Added 19 Oct 2010
Updated 19 Oct 2010
Type Conference
Year 2008
Where FAW
Authors Michael Dom, Somnath Sikdar
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