For protein structure alignment and comparison, a lot of work has been done using RMSD as the distance measure, which has drawbacks under certain circumstances. Thus, the discrete Fréchet distance was recently applied to the problem of protein (backbone) structure alignment and comparison with promising results. Visualization is also important since protein chain backbones can have up to 500~600 α-carbon atoms which constitute the vertices in the comparison. Even with an excellent alignment, the similarity can be difficult to visualize. Thus, the chain pair simplification problem (CPS-3F) was proposed in 2008 to simultaneously simplify both chains with respect to each other under the discrete Fréchet distance. The complexity of CPS-3F is unknown, so heuristic methods have been developed. Here, we define a variation of CPS-3F, the constrained CPS-3F problem (CPS-3F+), and prove it is polynomially solvable by presenting a dynamic programming solution, which we prove is a factor-2 approximation for CPS-3F. We then compare the CPS-3F+ solutions with previous empirical results, and further demonstrate the benefits of the simplified comparisons. CPS based on the Hausdorff distance (CPS-2H) is NP-complete, and we prove that CPS-2H+ is also NP-complete. Finally, we discuss future work and implications along with a software library implementation, named FPACT (The Fréchet-based Protein Alignment & Comparison Toolkit).