{"paper":{"title":"Approximation algorithms for the vertex-weighted grade-of-service Steiner tree problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Alon Efrat, Faryad Darabi Sahneh, Richard Spence, Spencer Krieger, Stephen Kobourov","submitted_at":"2018-11-28T17:37:13Z","abstract_excerpt":"Given a graph $G = (V,E)$ and a subset $T \\subseteq V$ of terminals, a \\emph{Steiner tree} of $G$ is a tree that spans $T$. In the vertex-weighted Steiner tree (VST) problem, each vertex is assigned a non-negative weight, and the goal is to compute a minimum weight Steiner tree of $G$.\n  We study a natural generalization of the VST problem motivated by multi-level graph construction, the \\emph{vertex-weighted grade-of-service Steiner tree problem} (V-GSST), which can be stated as follows: given a graph $G$ and terminals $T$, where each terminal $v \\in T$ requires a facility of a minimum grade "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.11700","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"}