{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/2-fault-tolerant-strong-connectivity-oracles","title":"$2$-Fault-Tolerant Strong Connectivity Oracles","arxiv_id":"2311.00854","date":"2023-11-01","proceeding":null,"authors":["Loukas Georgiadis","Evangelos Kosinas","Daniel Tsokaktsis"],"abstract":"We study the problem of efficiently answering strong connectivity queries under two vertex failures. Given a directed graph $G$ with $n$ vertices, we provide a data structure with $O(nh)$ space and $O(h)$ query time, where $h$ is the height of a decomposition tree of $G$ into strongly connected subgraphs. This immediately implies data structures with $O(n \\log{n})$ space and $O(\\log{n})$ query time for graphs of constant treewidth, and $O(n^{3/2})$ space and $O(\\sqrt{n})$ query time for planar graphs. For general directed graphs, we give a refined version of our data structure that achieves $O(n\\sqrt{m})$ space and $O(\\sqrt{m})$ query time, where $m$ is the number of edges of the graph. We also provide some simple BFS-based heuristics that seem to work remarkably well in practice. In the experimental part, we first evaluate various methods to construct a decomposition tree with small height $h$ in practice. Then we provide efficient implementations of our data structures, and evaluate their empirical performance by conducting an extensive experimental study on graphs taken from real-world applications.","url_abs":"https://arxiv.org/abs/2311.00854v2","url_pdf":"https://arxiv.org/pdf/2311.00854v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"2-fault-tolerant-strong-connectivity-oracles","repo_url":"https://github.com/dtsok/2-ft-sc-o","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}