Improved bounds for covering general polygons with rectangles
Proc. of the seventh conference on Foundations of software technology and theoretical computer science
Approximation algorithms for hitting objects with straight lines
Discrete Applied Mathematics
On the hardness of approximating minimization problems
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Efficient probabilistically checkable proofs and applications to approximations
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Approximation algorithms for NP-hard problems
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Improved low-degree testing and its applications
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Covering rectilinear polygons with axis-parallel rectangles
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
A New Method of image Compression Using Irreducible Covers of Maximal Rectangles
IEEE Transactions on Software Engineering
Splitters and near-optimal derandomization
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Proof verification and hardness of approximation problems
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Connected sensor cover: self-organization of sensor networks for efficient query execution
IEEE/ACM Transactions on Networking (TON)
Note: A parameterized algorithm for the hyperplane-cover problem
Theoretical Computer Science
MAX-SNP hardness of MIN-PC and MASC-GP(n) problems
Pattern Recognition and Image Analysis
On guarding rectilinear domains
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
A distributed greedy algorithm for connected sensor cover in dense sensor networks
DCOSS'05 Proceedings of the First IEEE international conference on Distributed Computing in Sensor Systems
Covering a set of points with a minimum number of lines
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Removing local extrema from imprecise terrains
Computational Geometry: Theory and Applications
Approximation algorithms for a geometric set cover problem
Discrete Applied Mathematics
Mobility-assisted minimum connected cover in a wireless sensor network
Journal of Parallel and Distributed Computing
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 a restricted version of the general Set Covering problem in which each set in the given set system intersects with any other set in at most 1 element. We show that the Set Covering problem with intersection 1 cannot be approximated within a o(log n) factor in random polynomial time unless N P ⊆ ZTIME(nO(log log n)). We also observe that the main challenge in derandomizing this reduction lies in finding a hitting set for large volume combinatorial rectangles satisfying certain intersection properties. These properties are not satisfied by current methods of hitting set construction. An example of a Set Covering problem with the intersection 1 property is the problem of covering a given set of points in two or higher dimensions using straight lines; any two straight lines intersect in at most one point. The best approximation algorithm currently known for this problem has an approximation factor of θ(log n), and beating this bound seems hard. We observe that this problem is Max-SNP-Hard.