Low rank methods for network alignment

Network alignment is the problem of finding a common subgraph between two graphs, and more generally k graphs. The results of network alignment are often used for information transfer, which makes it a powerful tool for deducing information or insight about networks. Network alignment is tightly related to the subgraph isomorphism problem which is known to be NP-hard, this makes the network alignment problem supremely hard in practice. Some algorithms have been devised to approach it via solving a form of a relaxed version of the NP-hard problem or by defining certain heuristic measures. These algorithms normally work well for problems when there is some form of prior known similarity between the nodes of the graphs to be aligned. The absence of such information makes the problem more challenging. In this scenario, these algorithms would often require much more time to finish executing, and even fail sometimes. The version of network alignment that this thesis tackles is the one when such prior similarity measures are absent. In this thesis, we address three versions of network alignment: (i) multimoal network alignment, (ii) standard pairwise network alignment, and (iii) multiple network alignment. A key common component of the algorithms presented in this thesis is exploiting a low rank structure in the network alignment problem and thus producing algorithms that run much faster than classic network alignment algorithms.