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 any input, is O(n log n). This is optimal in the algebraic decision tree model of computation.
|Keywords||Computational geometry, Disk packing, Origami|
|Journal||Journal of Discrete Algorithms|
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