This paper proposes a parameterized algorithm for aligning two protein structures, in the case where one protein structure is represented by a contact map graph and the other by a contact map graph or a distance matrix. If the sequential order of alignment is not required, the time complexity is polynomial in the protein size and exponential with respect to two parameters Du Dl and Dc Dl , which usually can be treated as constants. In particular, Du is the distance threshold determining if two residues are in contact or not, Dc is the maximally allowed distance between two matched residues after two proteins are superimposed, and Dl is the minimum inter-residue distance in a typical protein. This result indicates that if both Du Dl and Dc Dl are small enough, then there is a polynomial-time approximation scheme for the non-sequential protein structure alignment problem. Empirically, both Du Dl and Dc Dl are very small and can be treated as constants. This result clearly demonstrates th...