{"paper":{"title":"Better Balance by Being Biased: A 0.8776-Approximation for Max Bisection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Konstantinos Georgiou, Per Austrin, Siavosh Benabbas","submitted_at":"2012-05-02T15:19:29Z","abstract_excerpt":"Recently Raghavendra and Tan (SODA 2012) gave a 0.85-approximation algorithm for the Max Bisection problem. We improve their algorithm to a 0.8776-approximation. As Max Bisection is hard to approximate within $\\alpha_{GW} + \\epsilon \\approx 0.8786$ under the Unique Games Conjecture (UGC), our algorithm is nearly optimal. We conjecture that Max Bisection is approximable within $\\alpha_{GW}-\\epsilon$, i.e., the bisection constraint (essentially) does not make Max Cut harder.\n  We also obtain an optimal algorithm (assuming the UGC) for the analogous variant of Max 2-Sat. Our approximation ratio f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0458","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"}