Approximation algorithms for spreading points

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 time. In the L2 metric, we give a quadratic time algorithm that gives an -approximation in general, and a ∼2.2393-approximation when all the disks are congruent.