A packing problem with applications to lettering of maps
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Approximation algorithms for dispersion problems
Journal of Algorithms
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation of Geometric Dispersion Problems
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
Geometric Systems of Disjoint Representatives
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Approximation algorithms for aligning points
Proceedings of the nineteenth annual symposium on Computational geometry
Hall's theorem for hypergraphs
Journal of Graph Theory
A fast algorithm for single processor scheduling
SFCS '78 Proceedings of the 19th Annual Symposium on Foundations of Computer Science
Approximation algorithms for maximum dispersion
Operations Research Letters
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We consider the problem of placing n points, each one inside its own, prespecified disk, with the objective of maximizing the distance between the closest pair of them. The disks can overlap and have different sizes. The problem is NP-hard and does not admit a PTAS. In the L∞ metric, we give a 2-approximation algorithm running in $O(n{\sqrt n}log^{2}n)$ time. In the L2 metric, similar ideas yield a quadratic time algorithm that gives an $\frac{8}{3}$-approximation in general, and a ~ 2.2393-approximation when all the disks are congruent.