Discrete Mathematics - Topics on domination
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
The budgeted maximum coverage problem
Information Processing Letters
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Exact Algorithms and Approximation Schemes for Base Station Placement Problems
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Polynomial-time approximation schemes for packing and piercing fat objects
Journal of Algorithms
Polynomial-Time Approximation Schemes for Geometric Intersection Graphs
SIAM Journal on Computing
The complexity of base station positioning in cellular networks
Discrete Applied Mathematics
Combination can be hard: approximability of the unique coverage problem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Improved Approximation Algorithms for Geometric Set Cover
Discrete & Computational Geometry
The parameterized complexity of the unique coverage problem
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Covering points by unit disks of fixed location
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Better approximation schemes for disk graphs
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Interference in cellular networks: the minimum membership set cover problem
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
The complexity of making unique choices: approximating 1-in-k SAT
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
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
The Budgeted Unique Coverage Problem and Color-Coding
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
Shifting Strategy for Geometric Graphs without Geometry
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Shifting strategy for geometric graphs without geometry
Journal of Combinatorial Optimization
A polynomial-time approximation scheme for the geometric unique coverage problem on unit squares
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Special Section on CAD/Graphics 2013: Geometric multi-covering
Computers and Graphics
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We present the first study on the approximability of geometric versions of the unique coverage problem and the minimum membership set cover problem. In the former problem, one is given a family of sets of elements from some universe and aims to select sets that maximize the number of elements contained in precisely one selected set. Unique Coverage has important applications in wireless networks and it is thus natural to consider it in a geometric setting. We use the well-known (unit) disk model for wireless networks and show that Unique Coverage remains NP-hard in this case and present a polynomial-time 1/18-approximation algorithm. This algorithm is extended to the budgeted low-coverage problem, where covering can element multiple times yields less profit and we have a fixed budget to 'buy' sets. We give an asymptotic FPTAS in case the disks have arbitrary size, but bounded ply. For the case that the geometric objects are arbitrary fat objects, we show that these problems are as hard to approximate as in the general case. In the minimum membership set cover problem, the goal is to cover all elements while minimizing the maximum number of sets in which any element is contained. For unit squares and unit disks, we show that the problem remains NP-hard and does not admit a polynomial-time approximation algorithm with ratio smaller than 2 unless P=NP. For unit squares, we give a 5-approximation algorithm for instances where the optimum objective value is bounded by a constant.