The Parameterized Complexity of the Rectangle Stabbing Problem and Its Variants
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
Parameterized Complexity of Stabbing Rectangles and Squares in the Plane
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Reduction rules deliver efficient FPT-algorithms for covering points with lines
Journal of Experimental Algorithmics (JEA)
Note: A parameterized algorithm for the hyperplane-cover problem
Theoretical Computer Science
Slightly superexponential parameterized problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The complexity of geometric problems in high dimension
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
On covering points with minimum turns
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
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An abstract NP-hard covering problem is presented and fixed-parameter tractable algorithms for this problem are described. The running times of the algorithms are expressed in terms of three parameters: $n$, the number of elements to be covered, $k$, the number of sets allowed in the covering, and $d$, the combinatorial dimension of the problem. The first algorithm is deterministic and has a running time of $O’(k^{dk}n)$. The second algorithm is also deterministic and has a running time of $O’(k^{d(k+1)}+n^{d+1})$. The third is a Monte-Carlo algorithm that runs in time $O’(\runtime)$ and is correct with probability $1-n^{-c}$. Here, the $O’$ notation hides factors that are polynomial in $d$. These algorithms lead to fixed-parameter tractable algorithms for many geometric and non-geometric covering problems.