{"paper":{"title":"Approximating Unique Games Using Low Diameter Graph Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Lap Chi Lau, Vedat Levi Alev","submitted_at":"2017-02-22T19:08:25Z","abstract_excerpt":"We design approximation algorithms for Unique Games when the constraint graph admits good low diameter graph decomposition. For the ${\\sf Max2Lin}_k$ problem in $K_r$-minor free graphs, when there is an assignment satisfying $1-\\varepsilon$ fraction of constraints, we present an algorithm that produces an assignment satisfying $1-O(r\\varepsilon)$ fraction of constraints, with the approximation ratio independent of the alphabet size. A corollary is an improved approximation algorithm for the ${\\sf MaxCut}$ problem for $K_r$-minor free graphs. For general Unique Games in $K_r$-minor free graphs,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06969","kind":"arxiv","version":5},"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"}