On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Fat Triangles Determine Linearly Many Holes
SIAM Journal on Computing
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Approximation algorithms
Lectures on Discrete Geometry
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Covering Rectilinear Polygons with Axis-Parallel Rectangles
SIAM Journal on Computing
A constant-factor approximation algorithm for optimal terrain guarding
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Improved Approximation Algorithms for Geometric Set Cover
Discrete & Computational Geometry
Restricted strip covering and the sensor cover problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Decomposition of multiple coverings into more parts
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Small-size ε-nets for axis-parallel rectangles and boxes
Proceedings of the forty-first annual ACM symposium on Theory of computing
Epsilon nets and union complexity
Proceedings of the twenty-fifth annual symposium on Computational geometry
PTAS for geometric hitting set problems via local search
Proceedings of the twenty-fifth annual symposium on Computational geometry
Approximation algorithms for maximum independent set of pseudo-disks
Proceedings of the twenty-fifth annual symposium on Computational geometry
On the set multi-cover problem in geometric settings
Proceedings of the twenty-fifth annual symposium on Computational geometry
Hitting sets when the VC-dimension is small
Information Processing Letters
Decomposing Coverings and the Planar Sensor Cover Problem
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
CJCDGCGT'05 Proceedings of the 7th China-Japan conference on Discrete geometry, combinatorics and graph theory
Energy efficient monitoring in sensor networks
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Constant-factor approximation for minimum-weight (connected) dominating sets in unit disk graphs
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
PTAS for weighted set cover on unit squares
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Algorithms for dominating set in disk graphs: breaking the log n Barrier
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
On capacitated set cover problems
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Weighted capacitated, priority, and geometric set cover via improved quasi-uniform sampling
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Improved bound for the union of fat triangles
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Geometric packing under non-uniform constraints
Proceedings of the twenty-eighth annual symposium on Computational geometry
Approximating low-dimensional coverage problems
Proceedings of the twenty-eighth annual symposium on Computational geometry
Weighted geometric set multi-cover via quasi-uniform sampling
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
A constant-factor approximation for multi-covering with disks
Proceedings of the twenty-ninth annual symposium on Computational geometry
Exact algorithms and APX-hardness results for geometric packing and covering problems
Computational Geometry: Theory and Applications
Octants are cover-decomposable into many coverings
Computational Geometry: Theory and Applications
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There has been much progress on geometric set cover problems, but most known techniques only apply to the unweighted setting. For the weighted setting, very few results are known with approximation guarantees better than that for the combinatorial set cover problem. In this article, we employ the idea of quasi-uniform sampling to obtain improved approximation guarantees in the weighted setting for a large class of problems for which such guarantees were known in the unweighted case. As a consequence of this sampling method, we obtain new results on the fractional set cover packing problem.