{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:2OSQEDLLDI7CSVA735RKBHZXER","short_pith_number":"pith:2OSQEDLL","schema_version":"1.0","canonical_sha256":"d3a5020d6b1a3e29541fdf62a09f37246fd888d0e9a62686294fd62a15db634b","source":{"kind":"arxiv","id":"1305.3584","version":1},"attestation_state":"computed","paper":{"title":"New Greedy Heuristics For Set Cover and Set Packing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"David Kordalewski","submitted_at":"2013-05-15T18:44:39Z","abstract_excerpt":"The Set Cover problem (SCP) and Set Packing problem (SPP) are standard NP-hard combinatorial optimization problems. Their decision problem versions are shown to be NP-Complete in Karp's 1972 paper. We specify a rough guide to constructing approximation heuristics that may have widespread applications and apply it to devise greedy approximation algorithms for SCP and SPP, where the selection heuristic is a variation of that in the standard greedy approximation algorithm. Our technique involves assigning to each input set a valuation and then selecting, in each round, the set whose valuation is "},"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":"1305.3584","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-05-15T18:44:39Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"dfe0ddddddc2cd10a5c0faeee46292fc0eb7d85de42cc7d8b97aa97ea89606df","abstract_canon_sha256":"f8c9c3be36653b677030cdfdb2d1bd36876d4a4395cbe93f02ebb93168050862"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:35.509768Z","signature_b64":"Xi9mzvoqeEZ7MOwD085aziy38ux58MVlaZ/AF9bHVW/Ar0Oq19bRd6zfuyjBCdLXyOGntqEz96H9NSbed+4zBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3a5020d6b1a3e29541fdf62a09f37246fd888d0e9a62686294fd62a15db634b","last_reissued_at":"2026-05-18T03:25:35.509279Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:35.509279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New Greedy Heuristics For Set Cover and Set Packing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"David Kordalewski","submitted_at":"2013-05-15T18:44:39Z","abstract_excerpt":"The Set Cover problem (SCP) and Set Packing problem (SPP) are standard NP-hard combinatorial optimization problems. Their decision problem versions are shown to be NP-Complete in Karp's 1972 paper. We specify a rough guide to constructing approximation heuristics that may have widespread applications and apply it to devise greedy approximation algorithms for SCP and SPP, where the selection heuristic is a variation of that in the standard greedy approximation algorithm. Our technique involves assigning to each input set a valuation and then selecting, in each round, the set whose valuation is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3584","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":"1305.3584","created_at":"2026-05-18T03:25:35.509358+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.3584v1","created_at":"2026-05-18T03:25:35.509358+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3584","created_at":"2026-05-18T03:25:35.509358+00:00"},{"alias_kind":"pith_short_12","alias_value":"2OSQEDLLDI7C","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"2OSQEDLLDI7CSVA7","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"2OSQEDLL","created_at":"2026-05-18T12:27:32.513160+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.25921","citing_title":"Curve Skeletonization in Continuous domain for Meshes and Point Clouds","ref_index":24,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2OSQEDLLDI7CSVA735RKBHZXER","json":"https://pith.science/pith/2OSQEDLLDI7CSVA735RKBHZXER.json","graph_json":"https://pith.science/api/pith-number/2OSQEDLLDI7CSVA735RKBHZXER/graph.json","events_json":"https://pith.science/api/pith-number/2OSQEDLLDI7CSVA735RKBHZXER/events.json","paper":"https://pith.science/paper/2OSQEDLL"},"agent_actions":{"view_html":"https://pith.science/pith/2OSQEDLLDI7CSVA735RKBHZXER","download_json":"https://pith.science/pith/2OSQEDLLDI7CSVA735RKBHZXER.json","view_paper":"https://pith.science/paper/2OSQEDLL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.3584&json=true","fetch_graph":"https://pith.science/api/pith-number/2OSQEDLLDI7CSVA735RKBHZXER/graph.json","fetch_events":"https://pith.science/api/pith-number/2OSQEDLLDI7CSVA735RKBHZXER/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2OSQEDLLDI7CSVA735RKBHZXER/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2OSQEDLLDI7CSVA735RKBHZXER/action/storage_attestation","attest_author":"https://pith.science/pith/2OSQEDLLDI7CSVA735RKBHZXER/action/author_attestation","sign_citation":"https://pith.science/pith/2OSQEDLLDI7CSVA735RKBHZXER/action/citation_signature","submit_replication":"https://pith.science/pith/2OSQEDLLDI7CSVA735RKBHZXER/action/replication_record"}},"created_at":"2026-05-18T03:25:35.509358+00:00","updated_at":"2026-05-18T03:25:35.509358+00:00"}