{"paper":{"title":"On the Integrality Gap of the Directed-Component Relaxation for Steiner Tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Mohammad Taghi Hajiaghayi, Shi Li","submitted_at":"2011-11-29T05:29:28Z","abstract_excerpt":"In this note, we show that the integrality gap of the $k$-Directed-Component- Relaxation($k$-DCR) LP for the Steiner tree problem, introduced by Byrka, Grandoni, Rothvob and Sanita (STOC 2010), is at most $\\ln(4)<1.39$. The proof is constructive: we can efficiently find a Steiner tree whose cost is at most $\\ln(4)$ times the cost of the optimal fractional $k$-restricted Steiner tree given by the $k$-DCR LP."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6698","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"}