On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
Discrete Mathematics - Topics on domination
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
Separators for sphere-packings and nearest neighbor graphs
Journal of the ACM (JACM)
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
NC-approximation schemes for NP- and PSPACE-hard problems for geometric graphs
Journal of Algorithms
Efficient Algorithms for the Domination Problems on Interval and Circular-Arc Graphs
SIAM Journal on Computing
Some APX-completeness results for cubic graphs
Theoretical Computer Science
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
Improved Approximation Algorithms for Geometric Set Cover
Discrete & Computational Geometry
The Complexity of Combinatorial Optimization Problems on $d$-Dimensional Boxes
SIAM Journal on Discrete Mathematics
Hitting sets when the VC-dimension is small
Information Processing Letters
Better approximation schemes for disk graphs
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
A PTAS for the minimum dominating set problem in unit disk graphs
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Parameterized complexity of independence and domination on geometric graphs
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
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
ICDCN '09 Proceedings of the 10th International Conference on Distributed Computing and Networking
Minimum Interference Planar Geometric Topology in Wireless Sensor Networks
WASA '09 Proceedings of the 4th International Conference on Wireless Algorithms, Systems, and Applications
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
Approximation algorithms for intersection graphs
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
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For intersection graphs of disks and other fat objects, polynomial-time approximation schemes are known for the independent set and vertex cover problems, but the existing techniques were not able to deal with the dominating set problem except in the special case of unit-size objects. We present approximation algorithms and inapproximability results that shed new light on the approximability of the dominating set problem in geometric intersection graphs. On the one hand, we show that for intersection graphs of arbitrary fat objects, the dominating set problem is as hard to approximate as for general graphs. For intersection graphs of arbitrary rectangles, we prove APX-hardness. On the other hand, we present a new general technique for deriving approximation algorithms for various geometric intersection graphs, yielding constant-factor approximation algorithms for r-regular polygons, where r is an arbitrary constant, for pairwise homothetic triangles, and for rectangles with bounded aspect ratio. For arbitrary fat objects with bounded ply, we get a (3 + Ɛ)-approximation algorithm.