Among the measures for quantifying the similarity between protein 3-D structures, contact map overlap (CMO) maximization deserved sustained attention during past decade. Despite this large involvement, the known algorithms possess a modest performance and are not applicable for large scale comparison. This paper offers a clear advance in this respect. We present a new integer programming model for CMO and propose an exact B&B algorithm with bounds obtained by a novel Lagrangian relaxation. The efficiency of the approach is demonstrated on a popular small benchmark (Skolnick set, 40 domains). On this set our algorithm significantly outperforms the best existing exact algorithms. Many hard CMO instances have been solved for the first time. To assess furthermore our approach, we constructed a large scale set of 300 protein domains. Computing the similarity measure for any of the 44850 couples, we obtained a classification in excellent agreement with SCOP.