{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:2WLYSDLRRUVO7WY3CKPC65DK3D","short_pith_number":"pith:2WLYSDLR","schema_version":"1.0","canonical_sha256":"d597890d718d2aefdb1b129e2f746ad8faf638cf579cff06a8839aa30c6e4032","source":{"kind":"arxiv","id":"1904.06141","version":1},"attestation_state":"computed","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1904.06141","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-12T10:04:58Z","cross_cats_sorted":[],"title_canon_sha256":"4087ec9c9982d6ec6693b1c88f078312921f6743fcc00de4e561df257a4cfeb8","abstract_canon_sha256":"fda4818ffeeeaba596890ff1c9c82e841bc11829feb7f5e94cab677d8b6a63b6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:43.979450Z","signature_b64":"uga1W4/IQG6Dj1jBzZSb0VyhRqi/lyH2mKULiouN2zHCgAOy/RjWSP1a7y/FB3RWxZ3jO2aatUkTQhgMQi3kAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d597890d718d2aefdb1b129e2f746ad8faf638cf579cff06a8839aa30c6e4032","last_reissued_at":"2026-05-17T23:48:43.978803Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:43.978803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1904.06141","created_at":"2026-05-17T23:48:43.978898+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.06141v1","created_at":"2026-05-17T23:48:43.978898+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.06141","created_at":"2026-05-17T23:48:43.978898+00:00"},{"alias_kind":"pith_short_12","alias_value":"2WLYSDLRRUVO","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"2WLYSDLRRUVO7WY3","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"2WLYSDLR","created_at":"2026-05-18T12:33:07.085635+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2WLYSDLRRUVO7WY3CKPC65DK3D","json":"https://pith.science/pith/2WLYSDLRRUVO7WY3CKPC65DK3D.json","graph_json":"https://pith.science/api/pith-number/2WLYSDLRRUVO7WY3CKPC65DK3D/graph.json","events_json":"https://pith.science/api/pith-number/2WLYSDLRRUVO7WY3CKPC65DK3D/events.json","paper":"https://pith.science/paper/2WLYSDLR"},"agent_actions":{"view_html":"https://pith.science/pith/2WLYSDLRRUVO7WY3CKPC65DK3D","download_json":"https://pith.science/pith/2WLYSDLRRUVO7WY3CKPC65DK3D.json","view_paper":"https://pith.science/paper/2WLYSDLR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.06141&json=true","fetch_graph":"https://pith.science/api/pith-number/2WLYSDLRRUVO7WY3CKPC65DK3D/graph.json","fetch_events":"https://pith.science/api/pith-number/2WLYSDLRRUVO7WY3CKPC65DK3D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2WLYSDLRRUVO7WY3CKPC65DK3D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2WLYSDLRRUVO7WY3CKPC65DK3D/action/storage_attestation","attest_author":"https://pith.science/pith/2WLYSDLRRUVO7WY3CKPC65DK3D/action/author_attestation","sign_citation":"https://pith.science/pith/2WLYSDLRRUVO7WY3CKPC65DK3D/action/citation_signature","submit_replication":"https://pith.science/pith/2WLYSDLRRUVO7WY3CKPC65DK3D/action/replication_record"}},"created_at":"2026-05-17T23:48:43.978898+00:00","updated_at":"2026-05-17T23:48:43.978898+00:00"}