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.

Extracted Key Phrases

15 Figures and Tables

Cite this paper

@article{Sadhu2015ApproximationAF, title={Approximation algorithms for the two-center problem of convex polygon}, author={Sanjib Sadhu and Sasanka Roy and Soumen Nandi and Anil Maheshwari and Subhas C. Nandy}, journal={CoRR}, year={2015}, volume={abs/1512.02356} }