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|We determine information theoretic conditions under which it is possible to partially recover the alignment used to generate a pair of sparse, correlated Erd˝os-R´enyi graphs. To prove our achievability result, we introduce the k-core alignment estimator. This estimator searches for an alignment in which the intersection of the correlated graphs using this alignment has a minimum degree of k. We prove a matching converse bound. As the number of vertices grows, recovery of the alignment for a fraction of the vertices tending to one is possible when the average degree of the intersection of the graph pair tends to infinity. It was previously known that exact alignment is possible when this average degree grows faster than the logarithm of the number of vertices.
|Cullina, Daniel, Kiyavash, Negar, Mittal, Prateek, Poor, H Vincent. (2020). Partial Recovery of Erdős-Rényi Graph Alignment via k-Core Alignment. Abstracts of the 2020 SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Systems, 10.1145/3393691.3394211
|Type of Material:
|Abstracts of the 2020 SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Systems
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