1. On seeded subgraph-to-subgraph matching: The ssSGM Algorithm and matchability information theory
- Author
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Meng, Lingyao, Lou, Mengqi, Lin, Jianyu, Lyzinski, Vince, and Fishkind, Donniell E.
- Subjects
Mathematics - Optimization and Control ,05C60, 05C80, 90C35 - 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., Comment: 27 pages, 16 figures
- Published
- 2023