Homology search methods are dominated by the central paradigm that sequence similarity is a proxy for common ancestry and, by extension, functional similarity. For determining sequence similarity in proteins, most widely used methods use models of sequence evolution and compare amino-acid strings in search for conserved linear stretches. Probabilistic models or sequence profiles capture the position-specific variation in an alignment of homologous sequences and can identify conserved motifs or domains. While profile-based search methods are generally more accurate than simple sequence comparison methods, they tend to be computationally more demanding. In recent years, several methods have emerged that perform protein similarity searches based on domain composition. However, few methods have considered the linear arrangements of domains when conducting similarity searches, despite strong evidence that domain order can harbour considerable functional and evolutionary signal.