Computing the similarity between two protein structures is a crucial task in molecular biology, and has been extensively investigated. Many protein structure comparison methods can be modeled as maximum clique problems in specific k-partite graphs, referred here as alignment graphs. In this paper, we propose a new protein structure comparison method based on internal distances (DAST), which main characteristic is that it generates alignments having RMSD smaller than any previously given threshold. DAST is posed as a maximum clique problem in an alignment graph, and in order to compute DAST's alignments, we also design an algorithm (ACF) for solving such maximum clique problems. We compare ACF with one of the fastest clique finder, recently conceived by Österg˙ard. On a popular benchmark (the Skolnick set) we observe that ACF is about 20 times faster in average than the Österg˙ard's algorithm. We then successfully use DAST's alignments to obtain automatic classification in very good agreement with SCOP.