{"paper":{"title":"Fast and simple connectivity in graph timelines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Adam Karczmarz, Jakub {\\L}\\k{a}cki","submitted_at":"2015-06-09T15:58:59Z","abstract_excerpt":"In this paper we study the problem of answering connectivity queries about a \\emph{graph timeline}. A graph timeline is a sequence of undirected graphs $G_1,\\ldots,G_t$ on a common set of vertices of size $n$ such that each graph is obtained from the previous one by an addition or a deletion of a single edge. We present data structures, which preprocess the timeline and can answer the following queries:\n  - forall$(u,v,a,b)$ -- does the path $u\\to v$ exist in each of $G_a,\\ldots,G_b$?\n  - exists$(u,v,a,b)$ -- does the path $u\\to v$ exist in any of $G_a,\\ldots,G_b$?\n  - forall2$(u,v,a,b)$ -- do"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02973","kind":"arxiv","version":1},"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"}