{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:WXCPYU3EQDTUNKK5RM7AV4NMKL","short_pith_number":"pith:WXCPYU3E","canonical_record":{"source":{"id":"1712.02103","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-12-06T09:42:34Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"b12abf524e4542f971f28181564659d65efe086d21e6bc6a93a011900c59d572","abstract_canon_sha256":"46371ea8663de96a6b57bc66756bd3fdb397cac8c6b88a42f3df98d5ea067364"},"schema_version":"1.0"},"canonical_sha256":"b5c4fc536480e746a95d8b3e0af1ac52f09e2645c8adf283eee6f16daf9ea8cb","source":{"kind":"arxiv","id":"1712.02103","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.02103","created_at":"2026-05-18T00:28:39Z"},{"alias_kind":"arxiv_version","alias_value":"1712.02103v1","created_at":"2026-05-18T00:28:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02103","created_at":"2026-05-18T00:28:39Z"},{"alias_kind":"pith_short_12","alias_value":"WXCPYU3EQDTU","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WXCPYU3EQDTUNKK5","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WXCPYU3E","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:WXCPYU3EQDTUNKK5RM7AV4NMKL","target":"record","payload":{"canonical_record":{"source":{"id":"1712.02103","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-12-06T09:42:34Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"b12abf524e4542f971f28181564659d65efe086d21e6bc6a93a011900c59d572","abstract_canon_sha256":"46371ea8663de96a6b57bc66756bd3fdb397cac8c6b88a42f3df98d5ea067364"},"schema_version":"1.0"},"canonical_sha256":"b5c4fc536480e746a95d8b3e0af1ac52f09e2645c8adf283eee6f16daf9ea8cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:39.179562Z","signature_b64":"Zt819oSnOGiFmHmELx2dopMLNXPSOq0UMVEP7Ud1V7hNkidk/7vCX/ttXzYJLTVzsKBf2TWCKEFmPwcNGNcCBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5c4fc536480e746a95d8b3e0af1ac52f09e2645c8adf283eee6f16daf9ea8cb","last_reissued_at":"2026-05-18T00:28:39.178898Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:39.178898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.02103","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":"2026-05-18T00:28:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZfpU3T+x6zXBY0+S8QvG+lpPtuJyuoR8Wjzn9TI7WUyUwYK6oe6+FOr1/n01j5OF/IgdQzas12QvSrEL9GPkBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:55:16.064850Z"},"content_sha256":"4c7f7f3876353bd5581253e1ee39ef4ee8de0e8b605e6ffd100f341b1d0cbecb","schema_version":"1.0","event_id":"sha256:4c7f7f3876353bd5581253e1ee39ef4ee8de0e8b605e6ffd100f341b1d0cbecb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:WXCPYU3EQDTUNKK5RM7AV4NMKL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact Algorithms With Worst-case Guarantee For Scheduling: From Theory to Practice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Lei Shang","submitted_at":"2017-12-06T09:42:34Z","abstract_excerpt":"This PhD thesis summarizes research works on the design of exact algorithms that provide a worst-case (time or space) guarantee for NP-hard scheduling problems. Both theoretical and practical aspects are considered with three main results reported. The first one is about a Dynamic Programming algorithm which solves the F3Cmax problem in O*(3^n) time and space. The algorithm is easily generalized to other flowshop problems and single machine scheduling problems. The second contribution is about a search tree method called Branch & Merge which solves the 1||SumTi problem with the time complexity"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02103","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":"2026-05-18T00:28:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FJVHOvjKZJXwZoe/ticd19zLQ/2IeH3pBHftTTFPBAIEv3oSnORObQcaJ0Izyn+ZYj8FAfPXnXy1qkbuvlkEAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:55:16.065507Z"},"content_sha256":"53d4e685d97fb480370da29a27c4e8f0fd3e2fab6db4978ed671c070c87935ae","schema_version":"1.0","event_id":"sha256:53d4e685d97fb480370da29a27c4e8f0fd3e2fab6db4978ed671c070c87935ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WXCPYU3EQDTUNKK5RM7AV4NMKL/bundle.json","state_url":"https://pith.science/pith/WXCPYU3EQDTUNKK5RM7AV4NMKL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WXCPYU3EQDTUNKK5RM7AV4NMKL/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":"2026-06-12T06:55:16Z","links":{"resolver":"https://pith.science/pith/WXCPYU3EQDTUNKK5RM7AV4NMKL","bundle":"https://pith.science/pith/WXCPYU3EQDTUNKK5RM7AV4NMKL/bundle.json","state":"https://pith.science/pith/WXCPYU3EQDTUNKK5RM7AV4NMKL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WXCPYU3EQDTUNKK5RM7AV4NMKL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WXCPYU3EQDTUNKK5RM7AV4NMKL","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":"46371ea8663de96a6b57bc66756bd3fdb397cac8c6b88a42f3df98d5ea067364","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-12-06T09:42:34Z","title_canon_sha256":"b12abf524e4542f971f28181564659d65efe086d21e6bc6a93a011900c59d572"},"schema_version":"1.0","source":{"id":"1712.02103","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.02103","created_at":"2026-05-18T00:28:39Z"},{"alias_kind":"arxiv_version","alias_value":"1712.02103v1","created_at":"2026-05-18T00:28:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02103","created_at":"2026-05-18T00:28:39Z"},{"alias_kind":"pith_short_12","alias_value":"WXCPYU3EQDTU","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WXCPYU3EQDTUNKK5","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WXCPYU3E","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:53d4e685d97fb480370da29a27c4e8f0fd3e2fab6db4978ed671c070c87935ae","target":"graph","created_at":"2026-05-18T00:28:39Z","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":"This PhD thesis summarizes research works on the design of exact algorithms that provide a worst-case (time or space) guarantee for NP-hard scheduling problems. Both theoretical and practical aspects are considered with three main results reported. The first one is about a Dynamic Programming algorithm which solves the F3Cmax problem in O*(3^n) time and space. The algorithm is easily generalized to other flowshop problems and single machine scheduling problems. The second contribution is about a search tree method called Branch & Merge which solves the 1||SumTi problem with the time complexity","authors_text":"Lei Shang","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-12-06T09:42:34Z","title":"Exact Algorithms With Worst-case Guarantee For Scheduling: From Theory to Practice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02103","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":"sha256:4c7f7f3876353bd5581253e1ee39ef4ee8de0e8b605e6ffd100f341b1d0cbecb","target":"record","created_at":"2026-05-18T00:28:39Z","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":"46371ea8663de96a6b57bc66756bd3fdb397cac8c6b88a42f3df98d5ea067364","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-12-06T09:42:34Z","title_canon_sha256":"b12abf524e4542f971f28181564659d65efe086d21e6bc6a93a011900c59d572"},"schema_version":"1.0","source":{"id":"1712.02103","kind":"arxiv","version":1}},"canonical_sha256":"b5c4fc536480e746a95d8b3e0af1ac52f09e2645c8adf283eee6f16daf9ea8cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5c4fc536480e746a95d8b3e0af1ac52f09e2645c8adf283eee6f16daf9ea8cb","first_computed_at":"2026-05-18T00:28:39.178898Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:39.178898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zt819oSnOGiFmHmELx2dopMLNXPSOq0UMVEP7Ud1V7hNkidk/7vCX/ttXzYJLTVzsKBf2TWCKEFmPwcNGNcCBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:39.179562Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.02103","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c7f7f3876353bd5581253e1ee39ef4ee8de0e8b605e6ffd100f341b1d0cbecb","sha256:53d4e685d97fb480370da29a27c4e8f0fd3e2fab6db4978ed671c070c87935ae"],"state_sha256":"468e81825fce99ff53bc473d6f9fbca56c4c066e42ee3dfe37affd012034b760"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nDWIe6XTAchWfrXr6JG/d6pwmAbb1Ia7svGawiVdu9IGN9/azgyoBPvgHxHYBQ8mzIhUzdUfynzYjnGQ3v9UCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T06:55:16.068593Z","bundle_sha256":"9b6e4be6802291e226931f32950df6025be5591bb69fa90270a5a1fe46fa2aa9"}}