Approximation algorithms for inscribing or circumscribing an axially symmetric polygon to a convex polygon

Given a convex polygon P with n vertices, we present algorithms to determine approximations of the largest axially symmetric convex polygon S contained in P, and the smallest such polygon S$\varepsilon>0$0 , we can find an axially symmetric convex polygon Q O((1/Ö{e})logn+1/e3/2)O((1)logn+132) and O((1/)log n+(1/2)log(1/)) respectively