{"paper":{"title":"An efficient strongly connected components algorithm in the fault tolerant model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Keerti Choudhary, Liam Roditty, Surender Baswana","submitted_at":"2016-10-13T10:20:51Z","abstract_excerpt":"In this paper we study the problem of maintaining the strongly connected components of a graph in the presence of failures. In particular, we show that given a directed graph $G=(V,E)$ with $n=|V|$ and $m=|E|$, and an integer value $k\\geq 1$, there is an algorithm that computes in $O(2^{k}n\\log^2 n)$ time for any set $F$ of size at most $k$ the strongly connected components of the graph $G\\setminus F$. The running time of our algorithm is almost optimal since the time for outputting the SCCs of $G\\setminus F$ is at least $\\Omega(n)$. The algorithm uses a data structure that is computed in a pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04010","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"}