Mutation region detection is the first step of searching for a disease gene and has facilitated the identification of several hundred human genes that can harbor mutations leading to a disease phenotype. Recently, the closest shared center problem (CSC) was proposed as a core to solve the mutation region detection problem when the pedigree is not given (Ma et al. in IEEE ACM Trans Comput Biol Bioinform 9(2):372–384, 2012). A ratio-2 approximation algorithm was proposed for the CSC problem in Ma et al. (IEEE ACM Trans Comput Biol Bioinform 9(2):372–384, 2012). In this paper, we will design a polynomial time approximation scheme for this problem.