Scalable Algorithms for Multiple Network Alignment

Huda Nassar, Georgios Kollias, Ananth Grama, David F. Gleich

Abstract: Multiple network alignment is the problem of identifying similar and related regions in a given set of networks. While there are a large number of effective techniques for pairwise problems with two networks that scale in terms of edges, these cannot be readily extended to align multiple networks as the computational complexity will tend to grow exponentially with the number of networks. In this manuscript we introduce a new multiple network alignment algorithm and framework that is effective at aligning thousands of networks with thousands of nodes. The key enabling technique of our algorithm is identifying an exact and easy to compute low-rank tensor structure inside of a principled heuristic procedure for pairwise network alignment called IsoRank. This can be combined with a new algorithm for $k$-dimensional matching problems on low-rank tensors to produce the alignment. We demonstrate results on synthetic and real-world problems that show our technique (i) is as good as or better than, in terms of quality, existing methods, when they work on small problems, while running considerably faster, and (ii) is able to scale to aligning a number of networks unreachable by current methods.