Approximation algorithms for hitting objects with straight lines
Discrete Applied Mathematics
Discrete & Computational Geometry
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Approximation Algorithms for Rectangle Stabbing and Interval Stabbing Problems
SIAM Journal on Discrete Mathematics
Approximation of a Geometric Set Covering Problem
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Approximation algorithms for capacitated rectangle stabbing
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Parameterized Complexity
Parameterized Complexity of Geometric Problems
The Computer Journal
Parameterized Complexity of Stabbing Rectangles and Squares in the Plane
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
On the parameterized complexity of some optimization problems related to multiple-interval graphs
Theoretical Computer Science
Fixed-Parameter algorithms for cochromatic number and disjoint rectangle stabbing
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Information and Computation
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We study an NP-complete geometric covering problem called d-Dimensional Rectangle Stabbing, where, given a set of axis-parallel d-dimensional hyperrectangles, a set of axis-parallel (d驴 1)-dimensional hyperplanes and a positive integer k, the question is whether one can select at most kof the hyperplanes such that every hyperrectangle is intersected by at least one of these hyperplanes. This problem is well-studied from the approximation point of view, while its parameterized complexity remained unexplored so far. Here we show, by giving a nontrivial reduction from a problem called Multicolored Clique, that for d驴 3 the problem is W[1]-hard with respect to the parameter k. For the case d= 2, whose parameterized complexity is still open, we consider several natural restrictions and show them to be fixed-parameter tractable.