{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:FCRCYD7YB5UJ6DF2NZSFUAMHTU","short_pith_number":"pith:FCRCYD7Y","schema_version":"1.0","canonical_sha256":"28a22c0ff80f689f0cba6e645a01879d3c82ba05af4eab20aa8e6ab1da4de900","source":{"kind":"arxiv","id":"1510.08551","version":1},"attestation_state":"computed","paper":{"title":"Scheduling under Linear Constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Kameng Nip, Zhenbo Wang, Zizhuo Wang","submitted_at":"2015-10-29T02:48:28Z","abstract_excerpt":"We introduce a parallel machine scheduling problem in which the processing times of jobs are not given in advance but are determined by a system of linear constraints. The objective is to minimize the makespan, i.e., the maximum job completion time among all feasible choices. This novel problem is motivated by various real-world application scenarios. We discuss the computational complexity and algorithms for various settings of this problem. In particular, we show that if there is only one machine with an arbitrary number of linear constraints, or there is an arbitrary number of machines with"},"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":"1510.08551","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-10-29T02:48:28Z","cross_cats_sorted":[],"title_canon_sha256":"d3b78fa4663f770a2bb656c409c2e315d27f097a791474bc0bb35d853d17acb7","abstract_canon_sha256":"70cab0cd97995b54b0cd7b030e6c8dcb555410ccbeaa515dff403b97fb0dba75"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:28.537751Z","signature_b64":"pfjP05d5fEKB88zxu3GcZdyz2UH35i7L314vc9SE0JHWvHcHOMSHqRrPcYAA3FHMUrqw4sBcFbqc6xLByJuKDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28a22c0ff80f689f0cba6e645a01879d3c82ba05af4eab20aa8e6ab1da4de900","last_reissued_at":"2026-05-18T01:28:28.537196Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:28.537196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scheduling under Linear Constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Kameng Nip, Zhenbo Wang, Zizhuo Wang","submitted_at":"2015-10-29T02:48:28Z","abstract_excerpt":"We introduce a parallel machine scheduling problem in which the processing times of jobs are not given in advance but are determined by a system of linear constraints. The objective is to minimize the makespan, i.e., the maximum job completion time among all feasible choices. This novel problem is motivated by various real-world application scenarios. We discuss the computational complexity and algorithms for various settings of this problem. In particular, we show that if there is only one machine with an arbitrary number of linear constraints, or there is an arbitrary number of machines with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08551","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":"1510.08551","created_at":"2026-05-18T01:28:28.537269+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.08551v1","created_at":"2026-05-18T01:28:28.537269+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08551","created_at":"2026-05-18T01:28:28.537269+00:00"},{"alias_kind":"pith_short_12","alias_value":"FCRCYD7YB5UJ","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"FCRCYD7YB5UJ6DF2","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"FCRCYD7Y","created_at":"2026-05-18T12:29:19.899920+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/FCRCYD7YB5UJ6DF2NZSFUAMHTU","json":"https://pith.science/pith/FCRCYD7YB5UJ6DF2NZSFUAMHTU.json","graph_json":"https://pith.science/api/pith-number/FCRCYD7YB5UJ6DF2NZSFUAMHTU/graph.json","events_json":"https://pith.science/api/pith-number/FCRCYD7YB5UJ6DF2NZSFUAMHTU/events.json","paper":"https://pith.science/paper/FCRCYD7Y"},"agent_actions":{"view_html":"https://pith.science/pith/FCRCYD7YB5UJ6DF2NZSFUAMHTU","download_json":"https://pith.science/pith/FCRCYD7YB5UJ6DF2NZSFUAMHTU.json","view_paper":"https://pith.science/paper/FCRCYD7Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.08551&json=true","fetch_graph":"https://pith.science/api/pith-number/FCRCYD7YB5UJ6DF2NZSFUAMHTU/graph.json","fetch_events":"https://pith.science/api/pith-number/FCRCYD7YB5UJ6DF2NZSFUAMHTU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FCRCYD7YB5UJ6DF2NZSFUAMHTU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FCRCYD7YB5UJ6DF2NZSFUAMHTU/action/storage_attestation","attest_author":"https://pith.science/pith/FCRCYD7YB5UJ6DF2NZSFUAMHTU/action/author_attestation","sign_citation":"https://pith.science/pith/FCRCYD7YB5UJ6DF2NZSFUAMHTU/action/citation_signature","submit_replication":"https://pith.science/pith/FCRCYD7YB5UJ6DF2NZSFUAMHTU/action/replication_record"}},"created_at":"2026-05-18T01:28:28.537269+00:00","updated_at":"2026-05-18T01:28:28.537269+00:00"}