Applications of random sampling in computational geometry, II
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Discrete Mathematics - Topics on domination
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
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
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Approximation algorithms
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
On the Optimality of Planar and Geometric Approximation Schemes
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Approximation schemes for wireless networks
ACM Transactions on Algorithms (TALG)
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
Approximation Algorithms for Domatic Partitions of Unit Disk Graphs
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
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
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
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
Weighted capacitated, priority, and geometric set cover via improved quasi-uniform sampling
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Wireless coverage with disparate ranges
MobiHoc '11 Proceedings of the Twelfth ACM International Symposium on Mobile Ad Hoc Networking and Computing
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We consider the problem of finding a lowest cost dominating set in a given disk graph containing n disks. The problem has been extensively studied on subclasses of disk graphs, yet the best known approximation for disk graphs has remained O(log n) - a bound that is asymptotically no better than the general case. We improve the status quo in two ways: for the unweighted case, we show how to obtain a PTAS using the framework recently proposed (independently) by Mustafa and Ray [16] and by Chan and Har-Peled [4]; for the weighted case where each input disk has an associated rational weight with the objective of finding a minimum cost dominating set, we give a randomized algorithm that obtains a dominating set whose weight is within a factor 2O(log* n) of a minimum cost solution, with high probability - the technique follows the framework proposed recently by Varadarajan [19].