Finding exact and maximum occurrences of protein complexes in protein-protein interaction graphs

In the context of comparative analysis of protein-protein interaction graphs, we use a graph-based formalism to detect the preservation of a given protein complex G in the protein-protein interaction graph H of another species with respect to (w.r.t.) orthologous proteins. Two problems are considered: the Exact-(mu(G),mu(H))-Matching problem and the Max-(mu(G),mu(H))-Matching problem, where mu(G) (resp. mu(H)) denotes in both problems the maximum number of orthologous proteins in H (resp. G) of a protein in G (resp. H). Following [FLV04], the Exact-(PG, pH)-Matching problem asks for an injective homomorphism of G to H w.r.t. orthologous proteins. The optimization version is called the Max-(mu(G), mu(H))-Matching problem and is concerned with finding an injective mapping of a graph G to a graph H w.r.t. orthologous proteins that matches as many edges of G as possible. For both problems, the emphasis here is clearly on bounded degree graphs and extremal small values of parameters mu(G) and mu(H).