A probabilistic analysis of the maximal covering location problem
Discrete Applied Mathematics - Special issue: local optimization
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
Approximation algorithms for NP-hard problems
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
The budgeted maximum coverage problem
Information Processing Letters
Selecting forwarding neighbors in wireless Ad Hoc networks
DIALM '01 Proceedings of the 5th international workshop on Discrete algorithms and methods for mobile computing and communications
Improved Approximation Algorithms for Geometric Set Cover
Discrete & Computational Geometry
On the Optimality of Planar and Geometric Approximation Schemes
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
A 5+epsilon (Porson)-approximation algorithm for minimum weighted dominating set in unit disk graph
Theoretical Computer Science
Multiobjective Disk Cover Admits a PTAS
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
PTAS for geometric hitting set problems via local search
Proceedings of the twenty-fifth annual symposium on Computational geometry
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
Covering points by unit disks of fixed location
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Domination in geometric intersection graphs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Weighted geometric set cover via quasi-uniform sampling
Proceedings of the forty-second ACM symposium on Theory of computing
Parameterized complexity of independence and domination on geometric graphs
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
A (4+ε)-approximation for the minimum-weight dominating set problem in unit disk graphs
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
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
Exact algorithms and APX-hardness results for geometric packing and covering problems
Computational Geometry: Theory and Applications
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We study the planar version of Minimum-Weight Set Cover, where one has to cover a given set of points with a minimum-weight subset of a given set of planar objects. For the unit-weight case, one PTAS (on disks) is known. For arbitrary weights however, the problem appears much harder, and in particular no PTASs are known. We present the first PTAS for Weighted Geometric Set Cover on planar objects, namely on axis-parallel unit squares. By extending the algorithm, we also obtain a PTAS for Minimum-Weight Dominating Set on intersection graphs of unit squares and Geometric Budgeted Maximum Coverage on unit squares. The running time of the developed algorithms is optimal under the exponential time hypothesis. We also show inapproximability results for Geometric Set Cover on various object shapes that are more general than unit squares.