SIAM Journal on Scientific Computing, Ahead of Print.
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.

中文翻译：

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多网络对齐的可扩展算法

SIAM 科学计算杂志，提前印刷。
多网络对齐是在给定的网络集中识别相似和相关区域的问题。虽然有大量有效的技术可以解决两个网络在边缘方面的成对问题，但这些技术不能很容易地扩展到对齐多个网络，因为计算复杂度会随着网络的数量呈指数增长。在这篇手稿中，我们介绍了一种新的多网络对齐算法和框架，它可以有效地将数千个网络与数千个节点对齐。我们算法的关键启用技术是在称为 IsoRank 的成对网络对齐的原理启发式过程中识别精确且易于计算的低秩张量结构。这可以与低秩张量上 $k$ 维匹配问题的新算法相结合，以产生对齐。我们展示了合成和现实世界问题的结果，表明我们的技术 (i) 在质量方面与现有方法一样好或更好，当它们处理小问题时，运行速度要快得多，并且 (ii) 是能够扩展以对齐当前方法无法访问的许多网络。