Approximation algorithms for the two-center problem of convex polygon

Given a convex polygon P with n vertices, the two-center problem is to find two congruent closed disks of minimum radius such that they completely cover P . We propose an algorithm for this problem in the streaming setup, where the input stream is the vertices of the polygon in clockwise order. It produces a radius r satisfying r ≤ 2ropt using O(1) space, where ropt is the optimum solution. Next, we show that in non-streaming setup, we can improve the approximation factor by r ≤ 1.84ropt, maintaining the time complexity of the algorithm to O(n), and using O(1) extra space in addition to the space required for storing the input.