Fast algorithms for shortest paths in planar graphs, with applications
SIAM Journal on Computing
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Topics in computational geometry
Topics in computational geometry
Selecting forwarding neighbors in wireless ad hoc networks
Mobile Networks and Applications - Discrete algorithms and methods for mobile computing and communications
Improved Approximation Algorithms for Geometric Set Cover
Discrete & Computational Geometry
A linear work, O(n1/6) time, parallel algorithm for solving planar Laplacians
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
PTAS for geometric hitting set problems via local search
Proceedings of the twenty-fifth annual symposium on Computational geometry
Covering points by unit disks of fixed location
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Improved Results on Geometric Hitting Set Problems
Discrete & Computational Geometry
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
Optimized relay node placement for connecting disjoint wireless sensor networks
Computer Networks: The International Journal of Computer and Telecommunications Networking
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Given m unit disks and n points in the plane, the discrete unit disk cover problem is to select a minimum subset of the disks to cover the points. This problem is NP-hard [11] and the best previous practical solution is a 38-approximation algorithm by Carmi et al. [4]. We first consider the line-separable discrete unit disk cover problem (the set of disk centres can be separated from the set of points by a line) for which we present an O(m 2 n)-time algorithm that finds an exact solution. Combining our line-separable algorithm with techniques from the algorithm of Carmi et al. [4] results in an O(m 2 n 4) time 22-approximate solution to the discrete unit disk cover problem.