{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SENVPIMNBPEAQB6AW62R6L2ZMG","short_pith_number":"pith:SENVPIMN","canonical_record":{"source":{"id":"1710.10904","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-30T12:43:47Z","cross_cats_sorted":[],"title_canon_sha256":"8e43459e873f375fd48c78915429915629e009f769d383c2f6d86e6bd2393c52","abstract_canon_sha256":"36d226afd68cfd9683edf3cc885da2677bfbb9cd3b5ccbeb45c76d88204d5c70"},"schema_version":"1.0"},"canonical_sha256":"911b57a18d0bc80807c0b7b51f2f596183e8a1caf885fdaa9dc83d5f8bbd83e0","source":{"kind":"arxiv","id":"1710.10904","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10904","created_at":"2026-05-18T00:31:46Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10904v1","created_at":"2026-05-18T00:31:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10904","created_at":"2026-05-18T00:31:46Z"},{"alias_kind":"pith_short_12","alias_value":"SENVPIMNBPEA","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SENVPIMNBPEAQB6A","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SENVPIMN","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SENVPIMNBPEAQB6AW62R6L2ZMG","target":"record","payload":{"canonical_record":{"source":{"id":"1710.10904","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-30T12:43:47Z","cross_cats_sorted":[],"title_canon_sha256":"8e43459e873f375fd48c78915429915629e009f769d383c2f6d86e6bd2393c52","abstract_canon_sha256":"36d226afd68cfd9683edf3cc885da2677bfbb9cd3b5ccbeb45c76d88204d5c70"},"schema_version":"1.0"},"canonical_sha256":"911b57a18d0bc80807c0b7b51f2f596183e8a1caf885fdaa9dc83d5f8bbd83e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:46.126637Z","signature_b64":"LrGbnNccQEBxq8ORs0eTosJ0tcsbvqEJs1A11L3kSeigWFuu4Ak4pONKvVE/48OwYNZNWZe/oTQYtWj/QLE5Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"911b57a18d0bc80807c0b7b51f2f596183e8a1caf885fdaa9dc83d5f8bbd83e0","last_reissued_at":"2026-05-18T00:31:46.125977Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:46.125977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.10904","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:31:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"30eJDry9x8ljHX2DQwLPcehgV5wCkS4Y4RnOW/R5dcKc6AtyJui2CKiRcLV19NL5BF0f6BOLgrLyuTzjI955Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:08:46.907257Z"},"content_sha256":"de568774aa1c2adb19331ae428176fa976076e051ca58d7e294908db42e9c907","schema_version":"1.0","event_id":"sha256:de568774aa1c2adb19331ae428176fa976076e051ca58d7e294908db42e9c907"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SENVPIMNBPEAQB6AW62R6L2ZMG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An FPTAS of Minimizing Total Weighted Completion Time on Single Machine with Position Constraint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"(2) Management Science, (3) Department of Computer Science, 83 Tat Chee Avenue, Chicago, China), City University of Hong Kong, D-22043 Hamburg, F. Jaehn (2), G. Calinescu (1), Germany, Helmut Schmidt University -- University of the Federal Armed Forces Hamburg, Holstenhofweg 85, Hong Kong SAR, IL 60616, Illinois Institute of Technology, Kowloon, K. Wang (3) ((1) Department of Computer Science, M. Li (3), Operations Research, USA","submitted_at":"2017-10-30T12:43:47Z","abstract_excerpt":"In this paper we study the classical scheduling problem of minimizing the total weighted completion time on a single machine with the constraint that one specific job must be scheduled at a specified position. We give dynamic programs with pseudo-polynomial running time, and a fully polynomial-time approximation scheme (FPTAS)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10904","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:31:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RI2nOC1PypoQZWY1jkdeDCkpL8Go3Kw0ueBDA7Kaq6Us8pkjtxgvk93QXwTP19uxQ4JWJljIccaz7BWuT3aMDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:08:46.907925Z"},"content_sha256":"4c3fce9775449366df8727124228660e57d6b040cc96a1c8d53f4a768a3e5530","schema_version":"1.0","event_id":"sha256:4c3fce9775449366df8727124228660e57d6b040cc96a1c8d53f4a768a3e5530"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SENVPIMNBPEAQB6AW62R6L2ZMG/bundle.json","state_url":"https://pith.science/pith/SENVPIMNBPEAQB6AW62R6L2ZMG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SENVPIMNBPEAQB6AW62R6L2ZMG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T20:08:46Z","links":{"resolver":"https://pith.science/pith/SENVPIMNBPEAQB6AW62R6L2ZMG","bundle":"https://pith.science/pith/SENVPIMNBPEAQB6AW62R6L2ZMG/bundle.json","state":"https://pith.science/pith/SENVPIMNBPEAQB6AW62R6L2ZMG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SENVPIMNBPEAQB6AW62R6L2ZMG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SENVPIMNBPEAQB6AW62R6L2ZMG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"36d226afd68cfd9683edf3cc885da2677bfbb9cd3b5ccbeb45c76d88204d5c70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-30T12:43:47Z","title_canon_sha256":"8e43459e873f375fd48c78915429915629e009f769d383c2f6d86e6bd2393c52"},"schema_version":"1.0","source":{"id":"1710.10904","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10904","created_at":"2026-05-18T00:31:46Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10904v1","created_at":"2026-05-18T00:31:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10904","created_at":"2026-05-18T00:31:46Z"},{"alias_kind":"pith_short_12","alias_value":"SENVPIMNBPEA","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SENVPIMNBPEAQB6A","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SENVPIMN","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:4c3fce9775449366df8727124228660e57d6b040cc96a1c8d53f4a768a3e5530","target":"graph","created_at":"2026-05-18T00:31:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we study the classical scheduling problem of minimizing the total weighted completion time on a single machine with the constraint that one specific job must be scheduled at a specified position. We give dynamic programs with pseudo-polynomial running time, and a fully polynomial-time approximation scheme (FPTAS).","authors_text":"(2) Management Science, (3) Department of Computer Science, 83 Tat Chee Avenue, Chicago, China), City University of Hong Kong, D-22043 Hamburg, F. Jaehn (2), G. Calinescu (1), Germany, Helmut Schmidt University -- University of the Federal Armed Forces Hamburg, Holstenhofweg 85, Hong Kong SAR, IL 60616, Illinois Institute of Technology, Kowloon, K. Wang (3) ((1) Department of Computer Science, M. Li (3), Operations Research, USA","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-30T12:43:47Z","title":"An FPTAS of Minimizing Total Weighted Completion Time on Single Machine with Position Constraint"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10904","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:de568774aa1c2adb19331ae428176fa976076e051ca58d7e294908db42e9c907","target":"record","created_at":"2026-05-18T00:31:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"36d226afd68cfd9683edf3cc885da2677bfbb9cd3b5ccbeb45c76d88204d5c70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-30T12:43:47Z","title_canon_sha256":"8e43459e873f375fd48c78915429915629e009f769d383c2f6d86e6bd2393c52"},"schema_version":"1.0","source":{"id":"1710.10904","kind":"arxiv","version":1}},"canonical_sha256":"911b57a18d0bc80807c0b7b51f2f596183e8a1caf885fdaa9dc83d5f8bbd83e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"911b57a18d0bc80807c0b7b51f2f596183e8a1caf885fdaa9dc83d5f8bbd83e0","first_computed_at":"2026-05-18T00:31:46.125977Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:46.125977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LrGbnNccQEBxq8ORs0eTosJ0tcsbvqEJs1A11L3kSeigWFuu4Ak4pONKvVE/48OwYNZNWZe/oTQYtWj/QLE5Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:46.126637Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.10904","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de568774aa1c2adb19331ae428176fa976076e051ca58d7e294908db42e9c907","sha256:4c3fce9775449366df8727124228660e57d6b040cc96a1c8d53f4a768a3e5530"],"state_sha256":"47db099787647253dd63b05d2ef1de46c80234e41ad9bc1da974db64d94991b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"55d1JPM/AZypAUP0pRC0rLxtXf+c8iUyeIcGqcBW/Ms+sOK/DfLfCiHeNc+QkvBOBkBcU8mJeRUhTc6qb90aAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:08:46.911454Z","bundle_sha256":"a6462523c9913f816c34d97063804e0a3a331dc545c301585e5403613a38a123"}}