{"paper":{"title":"Partial Recovery of Erd\\H{o}s-R\\'enyi Graph Alignment via $k$-Core Alignment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.IT"],"primary_cat":"cs.IT","authors_text":"Daniel Cullina, H. Vincent Poor, Negar Kiyavash, Prateek Mittal","submitted_at":"2018-09-10T19:12:23Z","abstract_excerpt":"We determine information theoretic conditions under which it is possible to partially recover the alignment used to generate a pair of sparse, correlated Erd\\H{o}s-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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03553","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}