Abstract. With ever increasing amount of available data on protein-protein interaction (PPI) networks and research revealing that these networks evolve at a modular level, discovery of conserved patterns in these networks becomes an important problem. Recent algorithms on aligning PPI networks target simplified structures such as conserved pathways to render these problems computationally tractable. However, since conserved structures that are parts of functional modules and protein complexes generally correspond to dense subnets of the network, algorithms that are able to extract conserved patterns in terms of general graphs are necessary. With this motivation, we focus here on discovering protein sets that induce subnets that are highly conserved in the interactome of a pair of species. For this purpose, we develop a framework that formally defines the pairwise local alignment problem for PPI networks, models the problem as a graph optimization problem, and presents fast algorithms f...