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Here m denotes the number of rows of A.\n  This gives an O(ln m)-approximation algorithm for CIP -- minimum-cost covering"},"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":"cs/0205030","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cs.DS","submitted_at":"2002-05-18T00:23:17Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"34c9f49c92b4c056a6840c88697a37e47e5ae57c31c3ee377a6102531e868367","abstract_canon_sha256":"f2ed5a424b29810d38a746a40fc155ba4060cdd38e778c5fd536a586f1dc63d3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:54.020035Z","signature_b64":"quKcmRMgkLsOS3KA9rZpW1M/S5uGDBeg12GrZC1N5dstE2jiX7lV0ggYGihDRvOEARsu7qZwutBZd60tkVG6CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"148c276a14aa7913b83c00da6551e10082f9f36de1dc7ca3e55b639d88a7b581","last_reissued_at":"2026-05-18T01:59:54.019556Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:54.019556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximation Algorithms for Covering/Packing Integer Programs","license":"","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Neal E. 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