{"paper":{"title":"A Note on Max $k$-Vertex Cover: Faster FPT-AS, Smaller Approximate Kernel and Improved Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Pasin Manurangsi","submitted_at":"2018-10-09T03:16:12Z","abstract_excerpt":"In Maximum $k$-Vertex Cover (Max $k$-VC), the input is an edge-weighted graph $G$ and an integer $k$, and the goal is to find a subset $S$ of $k$ vertices that maximizes the total weight of edges covered by $S$. Here we say that an edge is covered by $S$ iff at least one of its endpoints lies in $S$.\n  We present an FPT approximation scheme (FPT-AS) that runs in $(1/\\epsilon)^{O(k)} poly(n)$ time for the problem, which improves upon Gupta et al.'s $(k/\\epsilon)^{O(k)} poly(n)$-time FPT-AS [SODA'18, FOCS'18]. Our algorithm is simple: just use brute force to find the best $k$-vertex subset among"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03792","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"}