{"paper":{"title":"Computing and Testing Small Vertex Connectivity in Near-Linear Time and Queries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Danupon Nanongkai, Sorrachai Yingchareonthawornchai, Thatchaphol Saranurak","submitted_at":"2019-05-14T00:46:31Z","abstract_excerpt":"We present a new, simple, algorithm for the local vertex connectivity problem (LocalVC) introduced by Nanongkai~et~al. [STOC'19]. Roughly, given an undirected unweighted graph $G$, a seed vertex $x$, a target volume $\\nu$, and a target separator size $k$, the goal of LocalVC is to remove $k$ vertices `near' $x$ (in terms of $\\nu$) to disconnect the graph in `local time', which depends only on parameters $\\nu$ and $k$. In this paper, we present a simple randomized algorithm with running time $O(\\nu k^2)$ and correctness probability $2/3$.\n  Plugging our new localVC algorithm in the generic fram"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.05329","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"}