{"paper":{"title":"Fixed-Parameter and Approximation Algorithms: A New Look","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Guy Kortsarz, MohammadTaghi Hajiaghayi, Rajesh Chitnis","submitted_at":"2013-08-15T22:17:59Z","abstract_excerpt":"A Fixed-Parameter Tractable (\\FPT) $\\rho$-approximation algorithm for a minimization (resp. maximization) parameterized problem $P$ is an FPT algorithm that, given an instance $(x, k)\\in P$ computes a solution of cost at most $k \\cdot \\rho(k)$ (resp. $k/\\rho(k)$) if a solution of cost at most (resp. at least) $k$ exists; otherwise the output can be arbitrary. For well-known intractable problems such as the W[1]-hard {Clique} and W[2]-hard {Set Cover} problems, the natural question is whether we can get any \\FPT-approximation. It is widely believed that both {Clique} and {Set-Cover} admit no FP"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3520","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"}