{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:7AUNNLH3SZIJSOIY6MFADD2LPC","short_pith_number":"pith:7AUNNLH3","schema_version":"1.0","canonical_sha256":"f828d6acfb9650993918f30a018f4b7894b74c43f962b98abe0f3d65aea2a61b","source":{"kind":"arxiv","id":"1110.1896","version":1},"attestation_state":"computed","paper":{"title":"Restricted Parameter Range Promise Set Cover Problems Are Easy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Hao Chen","submitted_at":"2011-10-10T00:40:28Z","abstract_excerpt":"Let $({\\bf U},{\\bf S},d)$ be an instance of Set Cover Problem, where ${\\bf U}=\\{u_1,...,u_n\\}$ is a $n$ element ground set, ${\\bf S}=\\{S_1,...,S_m\\}$ is a set of $m$ subsets of ${\\bf U}$ satisfying $\\bigcup_{i=1}^m S_i={\\bf U}$ and $d$ is a positive integer. In STOC 1993 M. Bellare, S. Goldwasser, C. Lund and A. Russell proved the NP-hardness to distinguish the following two cases of ${\\bf GapSetCover_{\\eta}}$ for any constant $\\eta > 1$. The Yes case is the instance for which there is an exact cover of size $d$ and the No case is the instance for which any cover of ${\\bf U}$ from ${\\bf S}$ ha"},"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":"1110.1896","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-10-10T00:40:28Z","cross_cats_sorted":[],"title_canon_sha256":"6d3b42e0b96ae127e44efa05423b07dd76e459b46d13dbb9c5813dcf191e19fc","abstract_canon_sha256":"529826d0a0cf6f08a58edc12b38f59953af5ca9648180096aecad59cbbd99d69"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:19.387642Z","signature_b64":"o6LXEd//c1mrTO4GPEyxlDoHL3IZJG6gbSWwPV1gvypSYz2fxeC4/O0fYLU3l7chggXH4PQoG8y8v3NInU12BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f828d6acfb9650993918f30a018f4b7894b74c43f962b98abe0f3d65aea2a61b","last_reissued_at":"2026-05-18T04:11:19.387187Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:19.387187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Restricted Parameter Range Promise Set Cover Problems Are Easy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Hao Chen","submitted_at":"2011-10-10T00:40:28Z","abstract_excerpt":"Let $({\\bf U},{\\bf S},d)$ be an instance of Set Cover Problem, where ${\\bf U}=\\{u_1,...,u_n\\}$ is a $n$ element ground set, ${\\bf S}=\\{S_1,...,S_m\\}$ is a set of $m$ subsets of ${\\bf U}$ satisfying $\\bigcup_{i=1}^m S_i={\\bf U}$ and $d$ is a positive integer. In STOC 1993 M. Bellare, S. Goldwasser, C. Lund and A. Russell proved the NP-hardness to distinguish the following two cases of ${\\bf GapSetCover_{\\eta}}$ for any constant $\\eta > 1$. The Yes case is the instance for which there is an exact cover of size $d$ and the No case is the instance for which any cover of ${\\bf U}$ from ${\\bf S}$ ha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1896","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":"1110.1896","created_at":"2026-05-18T04:11:19.387250+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.1896v1","created_at":"2026-05-18T04:11:19.387250+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1896","created_at":"2026-05-18T04:11:19.387250+00:00"},{"alias_kind":"pith_short_12","alias_value":"7AUNNLH3SZIJ","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"7AUNNLH3SZIJSOIY","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"7AUNNLH3","created_at":"2026-05-18T12:26:22.705136+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/7AUNNLH3SZIJSOIY6MFADD2LPC","json":"https://pith.science/pith/7AUNNLH3SZIJSOIY6MFADD2LPC.json","graph_json":"https://pith.science/api/pith-number/7AUNNLH3SZIJSOIY6MFADD2LPC/graph.json","events_json":"https://pith.science/api/pith-number/7AUNNLH3SZIJSOIY6MFADD2LPC/events.json","paper":"https://pith.science/paper/7AUNNLH3"},"agent_actions":{"view_html":"https://pith.science/pith/7AUNNLH3SZIJSOIY6MFADD2LPC","download_json":"https://pith.science/pith/7AUNNLH3SZIJSOIY6MFADD2LPC.json","view_paper":"https://pith.science/paper/7AUNNLH3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.1896&json=true","fetch_graph":"https://pith.science/api/pith-number/7AUNNLH3SZIJSOIY6MFADD2LPC/graph.json","fetch_events":"https://pith.science/api/pith-number/7AUNNLH3SZIJSOIY6MFADD2LPC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7AUNNLH3SZIJSOIY6MFADD2LPC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7AUNNLH3SZIJSOIY6MFADD2LPC/action/storage_attestation","attest_author":"https://pith.science/pith/7AUNNLH3SZIJSOIY6MFADD2LPC/action/author_attestation","sign_citation":"https://pith.science/pith/7AUNNLH3SZIJSOIY6MFADD2LPC/action/citation_signature","submit_replication":"https://pith.science/pith/7AUNNLH3SZIJSOIY6MFADD2LPC/action/replication_record"}},"created_at":"2026-05-18T04:11:19.387250+00:00","updated_at":"2026-05-18T04:11:19.387250+00:00"}