Algorithmic Aspects of Protein Structure Similarity

We show that calculating contact map overlap (a measure of similarity of protein structures) is NPhard, but can be solved in polynomial time for several interesting and relevant special cases. We identify an important special case of this problem corresponding to self-avoiding walks, and prove a decomposition theorem and a corollary approximation result for this special case. These are the rst approximation algorithms with guaranteed error bounds, and NPcompleteness results in the literature in the area of protein structure alignment/fold recognition for measures of structure similarity of practical interest.