Identifying structurally similar proteins with different chain topologies can aid studies in homology modeling, protein folding, protein design, and protein evolution. These include circular permuted protein structures, and the more general cases of non-cyclic permutations between similar structures, which are related by non-topological rearrangement beyond circular permutation. We present a method based on an approximation algorithm that finds sequence-order independent structural alignments that are close to optimal. We formulate the structural alignment problem as a special case of the maximum-weight independent set problem, and solve this computationally intensive problem approximately by iteratively solving relaxations of a corresponding integer programming problem. The resulting structural alignment is sequence order independent. Our method is also insensitive to insertions, deletions, and gaps.