Computational geometry: an introduction
Computational geometry: an introduction
Approximation algorithms for hitting objects with straight lines
Discrete Applied Mathematics
The exact fitting problem in higher dimensions
Computational Geometry: Theory and Applications
Rectilinear and polygonal p-piercing and p-center problems
Proceedings of the twelfth annual symposium on Computational geometry
Rectilinear p-piercing problems
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Exact and approximation algorithms for clustering
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Vertex cover: further observations and further improvements
Journal of Algorithms
Hardness of Set Cover with Intersection 1
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
Parameterized Complexity
Reduction rules deliver efficient FPT-algorithms for covering points with lines
Journal of Experimental Algorithmics (JEA)
Covering a set of points with a minimum number of lines
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
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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 running time O驴 (kdkn). The second algorithm is also deterministic and has running time O驴(kd(k+1) + nd+1). The third is a Monte-Carlo algorithm that runs in time O驴(kd(k+1))+c2dk驴(d+1)/2驴 驴(d+1)/2驴 n log n) time and is correct with probability 1 - n-c. Here, the O驴 notation hides factors that are polynomial in d. These algorithms lead to fixed-parameter tractable algorithms for many geometric and non-geometric covering problems.