{"paper":{"title":"An Improved Integrality Gap for the Calinescu-Karloff-Rabani Relaxation for Multiway Cut","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Haris Angelidakis, Pasin Manurangsi, Yury Makarychev","submitted_at":"2016-11-17T01:57:54Z","abstract_excerpt":"We construct an improved integrality gap instance for the Calinescu-Karloff-Rabani LP relaxation of the Multiway Cut problem. In particular, for $k \\geqslant 3$ terminals, our instance has an integrality ratio of $6 / (5 + \\frac{1}{k - 1}) - \\varepsilon$, for every constant $\\varepsilon > 0$. For every $k \\geqslant 4$, our result improves upon a long-standing lower bound of $8 / (7 + \\frac{1}{k - 1})$ by Freund and Karloff (2000). Due to Manokaran et al.'s result (2008), our integrality gap also implies Unique Games hardness of approximating Multiway Cut of the same ratio."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05530","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"}