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)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Selecting forwarding neighbors in wireless ad hoc networks
Mobile Networks and Applications - Discrete algorithms and methods for mobile computing and communications
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
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
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Given a set P of n points and a set D of m unit disks on a 2-dimensional plane, the discrete unit disk cover (DUDC) problem is (i) to check whether each point in P is covered by at least one disk in D or not and (ii) if so, then find a minimum cardinality subset D* ⊆ D such that unit disks in D* cover all the points in P. The discrete unit disk cover problem is a geometric version of the general set cover problem which is NP-hard [14]. The general set cover problem is not approximable within c log |P|, for some constant c, but the DUDC problem was shown to admit a constant factor approximation. In this paper, we provide an algorithm with constant approximation factor 18. The running time of the proposed algorithm is O(n log n+m log m+mn). The previous best known tractable solution for the same problem was a 22-factor approximation algorithm with running time O(m2n4).