{"paper":{"title":"Fixed-parameter tractability of satisfying beyond the number of variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"A. Yeo, G. Gutin, M. Jones, R. Crowston, S. Saurabh, V. Raman","submitted_at":"2012-12-01T12:53:29Z","abstract_excerpt":"We consider a CNF formula $F$ as a multiset of clauses: $F=\\{c_1,..., c_m\\}$. The set of variables of $F$ will be denoted by $V(F)$. Let $B_F$ denote the bipartite graph with partite sets $V(F)$ and $F$ and with an edge between $v \\in V(F)$ and $c \\in F$ if $v \\in c$ or $\\bar{v} \\in c$. The matching number $\\nu(F)$ of $F$ is the size of a maximum matching in $B_F$. In our main result, we prove that the following parameterization of {\\sc MaxSat} (denoted by $(\\nu(F)+k)$-\\textsc{SAT}) is fixed-parameter tractable: Given a formula $F$, decide whether we can satisfy at least $\\nu(F)+k$ clauses in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0106","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"}