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 is posed as a maximum clique problem in an alignment graph. We also design an algorithm (ACF) for solving such maximum clique problems. ACF is first applied in the context of VAST, a software largely used in the National Center for Biotechnology Information, and then in the context of DAST. The obtained results on real protein alignment instances show that our algorithm is more than 37000 times faster than the original VAST clique solver which is based on Bron & Kerbosch algorithm. We furthermore compare ACF with one of the fastest clique finder, recently conceived by Ostergard. On a popular benchmark (the Skolnick set) we observe that ACF is about 20 times faster in average than the Ostergard's algorithm.