{"paper":{"title":"Graph Reconstruction from Noisy Random Subgraphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS","math.IT"],"primary_cat":"cs.IT","authors_text":"Andrew McGregor, Rik Sengupta","submitted_at":"2024-05-07T12:21:42Z","abstract_excerpt":"We consider the problem of reconstructing an undirected graph $G$ on $n$ vertices given multiple random noisy subgraphs or \"traces\". Specifically, a trace is generated by sampling each vertex with probability $p_v$, then taking the resulting induced subgraph on the sampled vertices, and then adding noise in the form of either (a) deleting each edge in the subgraph with probability $1-p_e$, or (b) deleting each edge with probability $f_e$ and transforming a non-edge into an edge with probability $f_e$. We show that, under mild assumptions on $p_v$, $p_e$ and $f_e$, if $G$ is selected uniformly "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.04261","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.04261/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}