Packing two disks into a polygonal environment

Abstract 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.

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