{"paper":{"title":"Optimizing Probabilistic Propagation in Graphs by Adding Edges","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"cs.DS","authors_text":"Aditya Bhaskara, Alex Crane, Blair D. Sullivan, Md Mumtahin Habib Ullah Mazumder, Prasanth Yalamanchili, Shweta Jain","submitted_at":"2024-07-02T19:28:31Z","abstract_excerpt":"Probabilistic graphs are an abstraction that allow us to study randomized propagation in graphs. In a probabilistic graph, each edge is \"active\" with a certain probability, independent of the other edges. For two vertices $u,v$, a classic quantity of interest, that we refer to as the proximity $\\mathcal{P}_{G}(u, v)$, is the probability that there exists a path between $u$ and $v$ all of whose edges are active. For a given subset of vertices $V_s$, the reach of $V_s$ is defined as the minimum over pairs $u \\in V_s$ and $v \\in V$ of the proximity $\\mathcal{P}_{G}(u,v)$. This quantity has been s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.02624","kind":"arxiv","version":3},"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/2407.02624/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"}