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oai:drops-oai.dagstuhl.de:18745 2024-03-06T11:02:37Z ddc:004 open_access

Maximal k-Edge-Connected Subgraphs in Almost-Linear Time for Small k Saranurak, Thatchaphol Yuan, Wuwei Graph algorithms Maximal k-edge-connected subgraphs Dynamic k-edge connectivity We give the first almost-linear time algorithm for computing the maximal k-edge-connected subgraphs of an undirected unweighted graph for any constant k. More specifically, given an n-vertex m-edge graph G = (V,E) and a number k = log^o(1) n, we can deterministically compute in O(m+n^{1+o(1)}) time the unique vertex partition {V_1,… ,V_z} such that, for every i, V_i induces a k-edge-connected subgraph while every superset V'_i ⊃ V_{i} does not. Previous algorithms with linear time work only when k ≤ 2 [Tarjan SICOMP'72], otherwise they all require Ω(m+n√n) time even when k = 3 [Chechik et al. SODA'17; Forster et al. SODA'20]. Our algorithm also extends to the decremental graph setting; we can deterministically maintain the maximal k-edge-connected subgraphs of a graph undergoing edge deletions in m^{1+o(1)} total update time. Our key idea is a reduction to the dynamic algorithm supporting pairwise k-edge-connectivity queries [Jin and Sun FOCS'20]. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Thatchaphol Saranurak and Wuwei Yuan 2023 Is Part Of LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ESA.2023.92 urn:nbn:de:0030-drops-187451 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.92 eng https://creativecommons.org/licenses/by/4.0/legalcode