{"paper":{"title":"Low-rank binary matrix approximation in column-sum norm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Fahad Panolan, Fedor V. Fomin, Kirill Simonov, Petr A. Golovach","submitted_at":"2019-04-12T10:04:58Z","abstract_excerpt":"We consider $\\ell_1$-Rank-$r$ Approximation over GF(2), where for a binary $m\\times n$ matrix ${\\bf A}$ and a positive integer $r$, one seeks a binary matrix ${\\bf B}$ of rank at most $r$, minimizing the column-sum norm $||{\\bf A} -{\\bf B}||_1$. We show that for every $\\varepsilon\\in (0, 1)$, there is a randomized $(1+\\varepsilon)$-approximation algorithm for $\\ell_1$-Rank-$r$ Approximation over GF(2) of running time $m^{O(1)}n^{O(2^{4r}\\cdot \\varepsilon^{-4})}$. This is the first polynomial time approximation scheme (PTAS) for this problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.06141","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"}