{"paper":{"title":"Parameterized Inapproximability of Exact Cover and Nearest Codeword","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Patrick Lin, Venkatesan Guruswami","submitted_at":"2019-05-16T02:28:14Z","abstract_excerpt":"The $k$-ExactCover problem is a parameterized version of the ExactCover problem, in which we are given a universe $U$, a collection $S$ of subsets of $U$, and an integer $k$, and the task is to determine whether $U$ can be partitioned into $k$ sets in $S$. This is a natural extension of the well-studied SetCover problem; though in the parameterized regime we know it to be $W[1]$-complete in the exact case, its parameterized complexity with respect to approximability is not well understood.\n  We prove that, assuming ETH, for some $\\gamma > 0$ there is no time $f(k) \\cdot N^{\\gamma k}$ algorithm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.06503","kind":"arxiv","version":2},"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"}