Message Passing Algorithms for Sparse Network Alignment

TL;DR

This paper introduces a novel message passing algorithm for efficiently approximating solutions to sparse network alignment problems, capable of handling very large graphs with hundreds of thousands of vertices.

Contribution

It presents a new message passing approach tailored for sparse network alignment, improving computational efficiency and scalability over existing methods.

Findings

The algorithm performs well on synthetic and real-world datasets.

It outperforms two leading solvers in accuracy and speed.

Effective on large-scale graphs with hundreds of thousands of vertices.

Abstract

Network alignment generalizes and unifies several approaches for forming a matching or alignment between the vertices of two graphs. We study a mathematical programming framework for network alignment problem and a sparse variation of it where only a small number of matches between the vertices of the two graphs are possible. We propose a new message passing algorithm that allows us to compute, very efficiently, approximate solutions to the sparse network alignment problems with graph sizes as large as hundreds of thousands of vertices. We also provide extensive simulations comparing our algorithms with two of the best solvers for network alignment problems on two synthetic matching problems, two bioinformatics problems, and three large ontology alignment problems including a multilingual problem with a known labeled alignment.