{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:5K2TQFNLLZRZMBHYEBZTCK6IKI","short_pith_number":"pith:5K2TQFNL","schema_version":"1.0","canonical_sha256":"eab53815ab5e639604f82073312bc852376c3c09aca7dbf2bc8efa3b5f3ef182","source":{"kind":"arxiv","id":"1012.3295","version":1},"attestation_state":"computed","paper":{"title":"Set Covering with Ordered Replacement -- Additive and Multiplicative Gaps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Friedrich Eisenbrand, Laura Sanit\\`a, Naonori Kakimura, Thomas Rothvo{\\ss}","submitted_at":"2010-12-15T11:56:31Z","abstract_excerpt":"We consider set covering problems where the underlying set system satisfies a particular replacement property w.r.t. a given partial order on the elements: Whenever a set is in the set system then a set stemming from it via the replacement of an element by a smaller element is also in the set system. Many variants of BIN PACKING that have appeared in the literature are such set covering problems with ordered replacement. We provide a rigorous account on the additive and multiplicative integrality gap and approximability of set covering with replacement. In particular we provide a polylogarithm"},"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":"1012.3295","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-12-15T11:56:31Z","cross_cats_sorted":[],"title_canon_sha256":"dc6e0a092e590863fb2b30146405bf09f6d60bd025320de042d364c7a7fb0829","abstract_canon_sha256":"c280ba7e9d21b78188f577ca8f582455ef6afb5865a1893f9db9f6f3e4e6b2ae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:23:07.170659Z","signature_b64":"mCqhtunAAaz1gUzA/vE7cxA2HLKYUR6bGdS4cwAgAa6REIkvqBQJ4QB4qYj6NGtaUWlv7/IeBoBACJ1348SECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eab53815ab5e639604f82073312bc852376c3c09aca7dbf2bc8efa3b5f3ef182","last_reissued_at":"2026-05-18T02:23:07.170064Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:23:07.170064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Set Covering with Ordered Replacement -- Additive and Multiplicative Gaps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Friedrich Eisenbrand, Laura Sanit\\`a, Naonori Kakimura, Thomas Rothvo{\\ss}","submitted_at":"2010-12-15T11:56:31Z","abstract_excerpt":"We consider set covering problems where the underlying set system satisfies a particular replacement property w.r.t. a given partial order on the elements: Whenever a set is in the set system then a set stemming from it via the replacement of an element by a smaller element is also in the set system. Many variants of BIN PACKING that have appeared in the literature are such set covering problems with ordered replacement. We provide a rigorous account on the additive and multiplicative integrality gap and approximability of set covering with replacement. In particular we provide a polylogarithm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3295","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":"1012.3295","created_at":"2026-05-18T02:23:07.170154+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.3295v1","created_at":"2026-05-18T02:23:07.170154+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3295","created_at":"2026-05-18T02:23:07.170154+00:00"},{"alias_kind":"pith_short_12","alias_value":"5K2TQFNLLZRZ","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_16","alias_value":"5K2TQFNLLZRZMBHY","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_8","alias_value":"5K2TQFNL","created_at":"2026-05-18T12:26:04.259169+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/5K2TQFNLLZRZMBHYEBZTCK6IKI","json":"https://pith.science/pith/5K2TQFNLLZRZMBHYEBZTCK6IKI.json","graph_json":"https://pith.science/api/pith-number/5K2TQFNLLZRZMBHYEBZTCK6IKI/graph.json","events_json":"https://pith.science/api/pith-number/5K2TQFNLLZRZMBHYEBZTCK6IKI/events.json","paper":"https://pith.science/paper/5K2TQFNL"},"agent_actions":{"view_html":"https://pith.science/pith/5K2TQFNLLZRZMBHYEBZTCK6IKI","download_json":"https://pith.science/pith/5K2TQFNLLZRZMBHYEBZTCK6IKI.json","view_paper":"https://pith.science/paper/5K2TQFNL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.3295&json=true","fetch_graph":"https://pith.science/api/pith-number/5K2TQFNLLZRZMBHYEBZTCK6IKI/graph.json","fetch_events":"https://pith.science/api/pith-number/5K2TQFNLLZRZMBHYEBZTCK6IKI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5K2TQFNLLZRZMBHYEBZTCK6IKI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5K2TQFNLLZRZMBHYEBZTCK6IKI/action/storage_attestation","attest_author":"https://pith.science/pith/5K2TQFNLLZRZMBHYEBZTCK6IKI/action/author_attestation","sign_citation":"https://pith.science/pith/5K2TQFNLLZRZMBHYEBZTCK6IKI/action/citation_signature","submit_replication":"https://pith.science/pith/5K2TQFNLLZRZMBHYEBZTCK6IKI/action/replication_record"}},"created_at":"2026-05-18T02:23:07.170154+00:00","updated_at":"2026-05-18T02:23:07.170154+00:00"}