Packing two disks into a polygonal environment
We consider the following problem. Given a polygon P, possibly with holes, and having n vertices, compute a pair of equal radius disks that do not intersect each other, are contained in P, and whose radius is maximized. Our main result is a simple randomized algorithm whose expected running time, on worst case input, is O(n log n). This is optimal in the algebraic decision tree model of computation.
Bose, P, Morin, P, & Vigneron, A. (Antoine). (2001). Packing two disks into a polygonal environment.