The Discrete and Mixed Minimax 2-Center Problem

Let P be a set of n points in the plane, the discrete minimax 2-center problem DMM2CP is that of finding two disks centered at $$\{p_1,p_2\} \in P$${p1,p2}∈P that minimize the maximum of two terms, namely, the Euclidean distance between two centers and the distance of any other point to the closer center. The mixed minimax 2-center problem MMM2CP is when one of the two centers is not in P. We present algorithms for solving the DMM2CP and MMM2CP. The time complexity of solving DMM2CP and MMM2CP are $$On^2\log n$$On2logn and $$On^2\log ^2 n$$On2log2n respectively.