Before revision:  (iii) The third algorithm, that has an approximation ratio of 27, guards all interior and boundary points of P in O(n^5) time  .
After revision:  (iii) The third algorithm, that has an approximation ratio of 27, guards all interior and boundary points of P in O(n^5) time . Further, these algorithms can be modified to obtain similar approximation ratios while using edge guards .