{"paper":{"title":"On the Integrality Gap of the Prize-Collecting Steiner Forest LP","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.OC"],"primary_cat":"cs.DM","authors_text":"Chaitanya Swamy, Jens Vygen, Jochen K\\\"onemann, Kanstantsin Pashkovich, Neil Olver, R. Ravi","submitted_at":"2017-06-20T17:41:43Z","abstract_excerpt":"In the prize-collecting Steiner forest (PCSF) problem, we are given an undirected graph $G=(V,E)$, edge costs $\\{c_e\\geq 0\\}_{e\\in E}$, terminal pairs $\\{(s_i,t_i)\\}_{i=1}^k$, and penalties $\\{\\pi_i\\}_{i=1}^k$ for each terminal pair; the goal is to find a forest $F$ to minimize $c(F)+\\sum_{i: (s_i,t_i)\\text{ not connected in }F}\\pi_i$. The Steiner forest problem can be viewed as the special case where $\\pi_i=\\infty$ for all $i$. It was widely believed that the integrality gap of the natural (and well-studied) linear-programming (LP) relaxation for PCSF is at most 2. We dispel this belief by sh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06565","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"}