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Faster Dynamic 2-Edge Connectivity in Directed Graphs

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Názov: Faster Dynamic 2-Edge Connectivity in Directed Graphs
Autori: Georgiadis, Loukas, Giannis, Konstantinos, Italiano, Giuseppe F.
Prispievatelia: Loukas Georgiadis and Konstantinos Giannis and Giuseppe F. Italiano
Informácie o vydavateľovi: Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2025.
Rok vydania: 2025
Predmety: Connectivity, dynamic algorithms, ddc:004, directed graphs
Popis: Let G be a directed graph with n vertices and m edges. We present a deterministic algorithm that maintains the 2-edge-connected components of G under a sequence of m edge insertions, with a total running time of O(n² log n). This significantly improves upon the previous best bound of O(mn) for graphs that are not very sparse. After each insertion, our algorithm supports the following queries with asymptotically optimal efficiency: - Test in constant time whether two query vertices v and w are 2-edge-connected in G. - Report in O(n) time all the 2-edge-connected components of G. Our approach builds on the recent framework of Georgiadis, Italiano, and Kosinas [FOCS 2024] for computing the 3-edge-connected components of a directed graph in linear time, which leverages the minset-poset technique of Gabow [TALG 2016]. Additionally, we provide a deterministic decremental algorithm for maintaining 2-edge-connectivity in strongly connected directed graphs. Given a sequence of m edge deletions, our algorithm maintains the 2-edge-connected components in total time n^(2+o(1)), while supporting the same queries as the incremental algorithm. This result assumes that the edges of a fixed spanning tree of G and of its reverse graph G^R are not deleted. Previously, the best known bound for the decremental problem was O(mn log n), obtained by a randomized algorithm without restrictions on the deletions. In contrast to prior dynamic algorithms for 2-edge-connectivity in directed graphs, our method avoids the incremental computation of dominator trees, thereby circumventing the known conditional lower bound of Ω(mn).
Druh dokumentu: Conference object
Popis súboru: application/pdf
Jazyk: English
DOI: 10.4230/lipics.esa.2025.26
Prístupová URL adresa: https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.26
Rights: CC BY
Prístupové číslo: edsair.od......1814..a36aaabc65a844bb3fd7477d5ed0e270
Databáza: OpenAIRE
Popis
Abstrakt:Let G be a directed graph with n vertices and m edges. We present a deterministic algorithm that maintains the 2-edge-connected components of G under a sequence of m edge insertions, with a total running time of O(n² log n). This significantly improves upon the previous best bound of O(mn) for graphs that are not very sparse. After each insertion, our algorithm supports the following queries with asymptotically optimal efficiency: - Test in constant time whether two query vertices v and w are 2-edge-connected in G. - Report in O(n) time all the 2-edge-connected components of G. Our approach builds on the recent framework of Georgiadis, Italiano, and Kosinas [FOCS 2024] for computing the 3-edge-connected components of a directed graph in linear time, which leverages the minset-poset technique of Gabow [TALG 2016]. Additionally, we provide a deterministic decremental algorithm for maintaining 2-edge-connectivity in strongly connected directed graphs. Given a sequence of m edge deletions, our algorithm maintains the 2-edge-connected components in total time n^(2+o(1)), while supporting the same queries as the incremental algorithm. This result assumes that the edges of a fixed spanning tree of G and of its reverse graph G^R are not deleted. Previously, the best known bound for the decremental problem was O(mn log n), obtained by a randomized algorithm without restrictions on the deletions. In contrast to prior dynamic algorithms for 2-edge-connectivity in directed graphs, our method avoids the incremental computation of dominator trees, thereby circumventing the known conditional lower bound of Ω(mn).
DOI:10.4230/lipics.esa.2025.26