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- W4287744524 abstract "In this paper, we consider the graph alignment problem, which is the problem of recovering, given two graphs, a one-to-one mapping between nodes that maximizes edge overlap. This problem can be viewed as a noisy version of the well-known graph isomorphism problem and appears in many applications, including social network deanonymization and cellular biology. Our focus here is on partial recovery, i.e., we look for a one-to-one mapping which is correct on a fraction of the nodes of the graph rather than on all of them, and we assume that the two input graphs to the problem are correlated ErdH{o}s-R'enyi graphs of parameters $(n,q,s)$. Our main contribution is then to give necessary and sufficient conditions on $(n,q,s)$ under which partial recovery is possible with high probability as the number of nodes $n$ goes to infinity. In particular, we show that it is possible to achieve partial recovery in the $nqs=Theta(1)$ regime under certain additional assumptions." @default.
- W4287744524 created "2022-07-26" @default.
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- W4287744524 date "2020-07-01" @default.
- W4287744524 modified "2023-09-26" @default.
- W4287744524 title "Partial Recovery in the Graph Alignment Problem" @default.
- W4287744524 doi "https://doi.org/10.48550/arxiv.2007.00533" @default.
- W4287744524 hasPublicationYear "2020" @default.
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