{"paper":{"title":"ETH-Hardness of Approximating 2-CSPs and Directed Steiner Network","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Irit Dinur, Pasin Manurangsi","submitted_at":"2018-05-10T07:46:07Z","abstract_excerpt":"We study the 2-ary constraint satisfaction problems (2-CSPs), which can be stated as follows: given a constraint graph $G=(V,E)$, an alphabet set $\\Sigma$ and, for each $\\{u, v\\}\\in E$, a constraint $C_{uv} \\subseteq \\Sigma\\times\\Sigma$, the goal is to find an assignment $\\sigma: V \\to \\Sigma$ that satisfies as many constraints as possible, where a constraint $C_{uv}$ is satisfied if $(\\sigma(u),\\sigma(v))\\in C_{uv}$.\n  While the approximability of 2-CSPs is quite well understood when $|\\Sigma|$ is constant, many problems are still open when $|\\Sigma|$ becomes super constant. One such problem "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03867","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"}