{"paper":{"title":"Connectivity Oracles for Planar Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Christian Wulff-Nilsen, Glencora Borradaile, Seth Pettie","submitted_at":"2012-04-18T18:46:35Z","abstract_excerpt":"We consider dynamic subgraph connectivity problems for planar graphs. In this model there is a fixed underlying planar graph, where each edge and vertex is either \"off\" (failed) or \"on\" (recovered). We wish to answer connectivity queries with respect to the \"on\" subgraph. The model has two natural variants, one in which there are $d$ edge/vertex failures that precede all connectivity queries, and one in which failures/recoveries and queries are intermixed.\n  We present a $d$-failure connectivity oracle for planar graphs that processes any $d$ edge/vertex failures in $sort(d,n)$ time so that co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4159","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"}