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)
NC-approximation schemes for NP- and PSPACE-hard problems for geometric graphs
Journal of Algorithms
The broadcast storm problem in a mobile ad hoc network
MobiCom '99 Proceedings of the 5th annual ACM/IEEE international conference on Mobile computing and networking
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Selecting forwarding neighbors in wireless ad hoc networks
Mobile Networks and Applications - Discrete algorithms and methods for mobile computing and communications
Algorithms for minimum m-connected k-tuple dominating set problem
Theoretical Computer Science
Approximation schemes for wireless networks
ACM Transactions on Algorithms (TALG)
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
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The following planar minimum disk cover problem is considered in this paper: given a set $\mathcal{D}$ of n disks and a set 驴 of m points in the Euclidean plane, where each disk covers a subset of points in 驴, to compute a subset of disks with minimum cardinality covering 驴. This problem is known to be NP-hard and an algorithm which approximates the optimal disk cover within a factor of (1+驴) in $\mathcal{O}(mn^{\mathcal{O}(\frac{1}{\epsilon^{2}}\log^{2}\frac{1}{\epsilon})})$ time is proposed in this paper. This work presents the first polynomial time approximation scheme for the minimum disk cover problem where the best known algorithm can approximate the optimal solution with a large constant factor. Further, several variants of the minimum disk cover problem such as the incongruent disk cover problem and the weighted disk cover problem are considered and approximation schemes are designed.