{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:RITFH5FSZ2IZZONFXLWLKEG2ZO","short_pith_number":"pith:RITFH5FS","schema_version":"1.0","canonical_sha256":"8a2653f4b2ce919cb9a5baecb510dacba571823cefdcd553fa3eb3165a5ea711","source":{"kind":"arxiv","id":"1507.01906","version":1},"attestation_state":"computed","paper":{"title":"Towards Tight Lower Bounds for Scheduling Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Abbas Bazzi, Ashkan Norouzi-Fard","submitted_at":"2015-07-07T18:04:24Z","abstract_excerpt":"We show a close connection between structural hardness for $k$-partite graphs and tight inapproximability results for scheduling problems with precedence constraints. Assuming a natural but nontrivial generalisation of the bipartite structural hardness result of Bansal and Khot, we obtain a hardness of $2-\\epsilon$ for the problem of minimising the makespan for scheduling precedence-constrained jobs with preemption on identical parallel machines. This matches the best approximation guarantee for this problem. Assuming the same hypothesis, we also obtain a super constant inapproximability resul"},"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":"1507.01906","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-07-07T18:04:24Z","cross_cats_sorted":[],"title_canon_sha256":"c6de87fad6130e5a4b01552fd7ee37c1286da01ce9fd0d8542bcc230118cceb9","abstract_canon_sha256":"e46fc007954d33659bfa03ea825132bf55f9341ce9a343a5562605c21ed4a617"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:12.072872Z","signature_b64":"FBauJQ4GNmX5UkqhcdSBteN/ZUGSegWO+H2LDaBqd0Sg9E/8x9OLsA2WNZ2W8aXBHjXeXx/+vptUCMrWS71eBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a2653f4b2ce919cb9a5baecb510dacba571823cefdcd553fa3eb3165a5ea711","last_reissued_at":"2026-05-18T01:37:12.072100Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:12.072100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Towards Tight Lower Bounds for Scheduling Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Abbas Bazzi, Ashkan Norouzi-Fard","submitted_at":"2015-07-07T18:04:24Z","abstract_excerpt":"We show a close connection between structural hardness for $k$-partite graphs and tight inapproximability results for scheduling problems with precedence constraints. Assuming a natural but nontrivial generalisation of the bipartite structural hardness result of Bansal and Khot, we obtain a hardness of $2-\\epsilon$ for the problem of minimising the makespan for scheduling precedence-constrained jobs with preemption on identical parallel machines. This matches the best approximation guarantee for this problem. Assuming the same hypothesis, we also obtain a super constant inapproximability resul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01906","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":"1507.01906","created_at":"2026-05-18T01:37:12.072251+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.01906v1","created_at":"2026-05-18T01:37:12.072251+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01906","created_at":"2026-05-18T01:37:12.072251+00:00"},{"alias_kind":"pith_short_12","alias_value":"RITFH5FSZ2IZ","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"RITFH5FSZ2IZZONF","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"RITFH5FS","created_at":"2026-05-18T12:29:39.896362+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/RITFH5FSZ2IZZONFXLWLKEG2ZO","json":"https://pith.science/pith/RITFH5FSZ2IZZONFXLWLKEG2ZO.json","graph_json":"https://pith.science/api/pith-number/RITFH5FSZ2IZZONFXLWLKEG2ZO/graph.json","events_json":"https://pith.science/api/pith-number/RITFH5FSZ2IZZONFXLWLKEG2ZO/events.json","paper":"https://pith.science/paper/RITFH5FS"},"agent_actions":{"view_html":"https://pith.science/pith/RITFH5FSZ2IZZONFXLWLKEG2ZO","download_json":"https://pith.science/pith/RITFH5FSZ2IZZONFXLWLKEG2ZO.json","view_paper":"https://pith.science/paper/RITFH5FS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.01906&json=true","fetch_graph":"https://pith.science/api/pith-number/RITFH5FSZ2IZZONFXLWLKEG2ZO/graph.json","fetch_events":"https://pith.science/api/pith-number/RITFH5FSZ2IZZONFXLWLKEG2ZO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RITFH5FSZ2IZZONFXLWLKEG2ZO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RITFH5FSZ2IZZONFXLWLKEG2ZO/action/storage_attestation","attest_author":"https://pith.science/pith/RITFH5FSZ2IZZONFXLWLKEG2ZO/action/author_attestation","sign_citation":"https://pith.science/pith/RITFH5FSZ2IZZONFXLWLKEG2ZO/action/citation_signature","submit_replication":"https://pith.science/pith/RITFH5FSZ2IZZONFXLWLKEG2ZO/action/replication_record"}},"created_at":"2026-05-18T01:37:12.072251+00:00","updated_at":"2026-05-18T01:37:12.072251+00:00"}