{"paper":{"title":"On Kernelization and Approximation for the Vector Connectivity Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.CC","authors_text":"Manuel Sorge, Stefan Kratsch","submitted_at":"2014-10-31T17:19:11Z","abstract_excerpt":"In the Vector Connectivity problem we are given an undirected graph $G=(V,E)$, a demand function $\\phi\\colon V\\to\\{0,\\ldots,d\\}$, and an integer $k$. The question is whether there exists a set $S$ of at most $k$ vertices such that every vertex $v\\in V\\setminus S$ has at least $\\phi(v)$ vertex-disjoint paths to $S$; this abstractly captures questions about placing servers or warehouses relative to demands. The problem is \\NP-hard already for instances with $d=4$ (Cicalese et al., arXiv '14), admits a log-factor approximation (Boros et al., Networks '14), and is fixed-parameter tractable in term"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8819","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"}