{"paper":{"title":"A Near-optimal Algorithm for Edge Connectivity-based Hierarchical Graph Decomposition","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DB","cs.SI"],"primary_cat":"cs.DS","authors_text":"Lijun Chang","submitted_at":"2017-11-25T04:43:12Z","abstract_excerpt":"Driven by many applications in graph analytics, the problem of computing $k$-edge connected components ($k$-ECCs) of a graph $G$ for a user-given $k$ has been extensively studied recently. In this paper, we investigate the problem of constructing the hierarchy of edge connectivity-based graph decomposition, which compactly represents the $k$-ECCs of a graph for all possible $k$ values. This is based on the fact that each $k$-ECC is entirely contained in a $(k-1)$-ECC. In contrast to the existing approaches that conduct the computation either in a bottom-up or a top-down manner, we propose a bi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09189","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"}