On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
A packing problem with applications to lettering of maps
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Sublinear-time parallel algorithms for matching and related problems
Journal of Algorithms
Ray shooting and parametric search
SIAM Journal on Computing
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Vertical Decomposition of Shallow Levels in 3-Dimensional Arrangements and Its Applications
SIAM Journal on Computing
Dynamic data structures for fat objects and their applications
Computational Geometry: Theory and Applications
Approximation algorithms for dispersion problems
Journal of Algorithms
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Geometric Systems of Disjoint Representatives
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Hall's theorem for hypergraphs
Journal of Graph Theory
Largest bounding box, smallest diameter, and related problems on imprecise points
Computational Geometry: Theory and Applications
Controlled Perturbation of sets of line segments in R2 with smart processing order
Computational Geometry: Theory and Applications
Note: Constrained k-center and movement to independence
Discrete Applied Mathematics
Nearest-neighbor searching under uncertainty
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Largest bounding box, smallest diameter, and related problems on imprecise points
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Systems of distant representatives in euclidean space
Proceedings of the twenty-ninth annual symposium on Computational geometry
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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(nnlog^2n) time. In the L"2 metric, we give a quadratic time algorithm that gives an 83-approximation in general, and a ~2.2393-approximation when all the disks are congruent.