{"paper":{"title":"Parameterized Exact and Approximation Algorithms for Maximum $k$-Set Cover and Related Satisfiability Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Edouard Bonnet, Florian Sikora, Vangelis Th. Paschos","submitted_at":"2013-09-18T17:40:53Z","abstract_excerpt":"Given a family of subsets $\\mathcal S$ over a set of elements~$X$ and two integers~$p$ and~$k$, Max k-Set Cover consists of finding a subfamily~$\\mathcal T \\subseteq \\mathcal S$ of cardinality at most~$k$, covering at least~$p$ elements of~$X$. This problem is W[2]-hard when parameterized by~$k$, and FPT when parameterized by $p$. We investigate the parameterized approximability of the problem with respect to parameters~$k$ and~$p$. Then, we show that Max Sat-k, a satisfiability problem generalizing Max k-Set Cover, is also FPT with respect to parameter~$p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4718","kind":"arxiv","version":3},"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"}