Background: Protein structure analysis and comparison are major challenges in structural bioinformatics. Despite the existence of many tools and algorithms, very few of them have managed to capture the intuitive understanding of protein structures developed in structural biology, especially in the context of rapid database searches. Such intuitions could help speed up similarity searches and make it easier to understand the results of such analyses. Results: We developed a TOPS++FATCAT algorithm that uses an intuitive description of the proteins' structures as captured in the popular TOPS diagrams to limit the search space of the aligned fragment pairs (AFPs) in the flexible alignment of protein structures performed by the FATCAT algorithm. The TOPS++FATCAT algorithm is faster than FATCAT by more than an order of magnitude with a minimal cost in classification and alignment accuracy. For beta-rich proteins its accuracy is better than FATCAT, because the TOPS+ strings models conta...