{"paper":{"title":"A Labeling Approach to Incremental Cycle Detection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC"],"primary_cat":"cs.DS","authors_text":"Amos Fiat, Edith Cohen, Haim Kaplan, Liam Roditty","submitted_at":"2013-10-31T04:41:06Z","abstract_excerpt":"In the \\emph{incremental cycle detection} problem arcs are added to a directed acyclic graph and the algorithm has to report if the new arc closes a cycle. One seeks to minimize the total time to process the entire sequence of arc insertions, or until a cycle appears.\n  In a recent breakthrough, Bender, Fineman, Gilbert and Tarjan \\cite{BeFiGiTa11} presented two different algorithms, with time complexity $O(n^2 \\log n)$ and $O(m \\cdot \\min \\{m^{1/2}, n^{2/3} \\})$, respectively.\n  In this paper we introduce a new technique for incremental cycle detection that allows us to obtain both bounds (up"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8381","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"}