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 any input, is O(n log n). This is optimal in the algebraic decision tree model of computation.

Computational geometry, Disk packing, Origami
dx.doi.org/10.1016/j.jda.2003.12.003
Journal of Discrete Algorithms
School of Computer Science

Bose, P, Morin, P, & Vigneron, A. (Antoine). (2004). Packing two disks into a polygonal environment. Journal of Discrete Algorithms, 2(3), 373–380. doi:10.1016/j.jda.2003.12.003