{"paper":{"title":"Parameterized Complexity of Satisfying Almost All Linear Equations over $\\mathbb{F}_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.DS"],"primary_cat":"cs.CC","authors_text":"A. Yeo, G. Gutin, M. Jones, R. Crowston","submitted_at":"2011-10-26T20:02:03Z","abstract_excerpt":"The problem MaxLin2 can be stated as follows. We are given a system $S$ of $m$ equations in variables $x_1,...,x_n$, where each equation is $\\sum_{i \\in I_j}x_i = b_j$ is assigned a positive integral weight $w_j$ and $x_i,b_j \\in \\mathbb{F}_2$, $I_j \\subseteq \\{1,2,...,n\\}$ for $j=1,...,m$. We are required to find an assignment of values to the variables in order to maximize the total weight of the satisfied equations.\n  Let $W$ be the total weight of all equations in $S$. We consider the following parameterized version of MaxLin2: decide whether there is an assignment satisfying equations of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5915","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"}