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.

Additional Metadata
Keywords Computational geometry, Disk packing, Origami
Persistent URL dx.doi.org/10.1016/j.jda.2003.12.003
Journal Journal of Discrete Algorithms
Citation
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