3.1 Predicate Join PatternsOur algo

3.1 Predicate Join Patterns
Our algorithm consists of mapping subgraphs of the query to subgraphs of the sources, and to this end the smallest subgraphs
we consider represent one atom’s “pattern”: they consist of one central predicate node and its (existential or distinguished) variable nodes. These primitive graphs are called predicate join patterns (or PJs) for the predicate they contain. Fig. 2(a) shows all predicate joins that the query Q contains, (i.e., all the query PJs). We will refer to greater subgoals than simple PJs as compound predicate join patterns or CPJs (PJs are also CPJs, although atomic ones). We can now restate Def. 3 using our graph terminology: A view CPJ covers a query CPJ if there is a graph homomorphism h, from the query graph to the view one, such that (1) h is the identity on predicate nodes and labeled edges and (2) if a query variable node u is distinguished then h(u) is also distinguished. For the query PJ for P1 in Fig. 2(a), all PJs that can potentially cover it, appear in Fig. 2(b)-(e). Notice that under this perspective: