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.

• Type: Conference
• Year: 2008
• Where: FAW
• Authors: Michael Dom, Somnath Sikdar
• Keywords: Algorithms, Axis-parallel D-dimensional Hyperrectangles, FAW 2008, NP-complete Geometric Covering, Parameterized Complexity