Planar point location using persistent search trees
Communications of the ACM
Optimal point location in a monotone subdivision
SIAM Journal on Computing
The exact fitting problem in higher dimensions
Computational Geometry: Theory and Applications
Hardness of Set Cover with Intersection 1
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
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
Improved FPT algorithms for rectilinear k-links spanning path
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Column Generation for the Minimum Hyperplanes Clustering Problem
INFORMS Journal on Computing
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We consider the minimum line covering problem: given a set S of n points in the plane, we want to find the smallest number l of straight lines needed to cover all n points in S. We show that this problem can be solved in O(n log l) time if l ∈ O(log1−εn), and that this is optimal in the algebraic computation tree model (we show that the Ω(nlog l) lower bound holds for all values of l up to $O(\sqrt n)$). Furthermore, a O(log l)-factor approximation can be found within the same O(n log l) time bound if $l \in O(\sqrt[4]{n})$. For the case when l ∈ Ω(log n) we suggest how to improve the time complexity of the exact algorithm by a factor exponential in l.