{"paper":{"title":"On Vertex Sparsifiers with Steiner Nodes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Julia Chuzhoy","submitted_at":"2012-04-12T21:37:48Z","abstract_excerpt":"Given an undirected graph $G=(V,E)$ with edge capacities $c_e\\geq 1$ for $e\\in E$ and a subset $T$ of $k$ vertices called terminals, we say that a graph $H$ is a quality-$q$ cut sparsifier for $G$ iff $T\\subseteq V(H)$, and for any partition $(A,B)$ of $T$, the values of the minimum cuts separating $A$ and $B$ in graphs $G$ and $H$ are within a factor $q$ from each other. We say that $H$ is a quality-$q$ flow sparsifier for $G$ iff $T\\subseteq V(H)$, and for any set $D$ of demands over the terminals, the values of the minimum edge congestion incurred by fractionally routing the demands in $D$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2844","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"}