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arXiv · 2306.04016

On seeded subgraph-to-subgraph matching: The ssSGM Algorithm and matchability information theory

Lingyao Meng·Mengqi Lou·Jianyu Lin·Vince Lyzinski·Donniell E. Fishkind
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Abstract

The subgraph-subgraph matching problem is, given a pair of graphs and a positive integer $K$, to find $K$ vertices in the first graph, $K$ vertices in the second graph, and a bijection between them, so as to minimize the number of adjacency disagreements across the bijection; it is ``seeded" if some of this bijection is fixed. The problem is intractable, and we present the ssSGM algorithm, which uses Frank-Wolfe methodology to efficiently find an approximate solution. Then, in the context of a generalized correlated random Bernoulli graph model, in which the pair of graphs naturally have a core of $K$ matched pairs of vertices, we provide and prove mild conditions for the subgraph-subgraph matching problem solution to almost always be the correct $K$ matched pairs of vertices.

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Lingyao Meng, Mengqi Lou, Jianyu Lin, Vince Lyzinski, Donniell E. Fishkind. 2023-06-06. On seeded subgraph-to-subgraph matching: The ssSGM Algorithm and matchability information theory. https://arxiv.org/abs/2306.04016

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