{"paper":{"title":"Parameterized Low-Rank Binary Matrix Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Fahad Panolan, Fedor V. Fomin, Petr A. Golovach","submitted_at":"2018-03-16T07:47:27Z","abstract_excerpt":"We provide a number of algorithmic results for the following family of problems: For a given binary m\\times n matrix A and integer k, decide whether there is a \"simple\" binary matrix B which differs from A in at most k entries. For an integer r, the \"simplicity\" of B is characterized as follows.\n  - Binary r-Means: Matrix B has at most r different columns. This problem is known to be NP-complete already for r=2. We show that the problem is solvable in time 2^{O(k\\log k)}\\cdot(nm)^{O(1)} and thus is fixed-parameter tractable parameterized by k. We prove that the problem admits a polynomial kern"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06102","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"}