{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ERBMLMDYZZT6ONRWPH5ECVIN7J","short_pith_number":"pith:ERBMLMDY","canonical_record":{"source":{"id":"1612.03339","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-10T20:36:09Z","cross_cats_sorted":[],"title_canon_sha256":"07b5ee52d066c6cf8ea090f453b8da20db626b5b2e833ecf837d9623ae16c120","abstract_canon_sha256":"c5beb941f79592b3aaddd1c1194848f3c265aebc40b530be5cae3f0d6d663e75"},"schema_version":"1.0"},"canonical_sha256":"2442c5b078ce67e7363679fa41550dfa4f88ad53cf3fe4dab5ba5ed5d497717c","source":{"kind":"arxiv","id":"1612.03339","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.03339","created_at":"2026-05-18T00:55:19Z"},{"alias_kind":"arxiv_version","alias_value":"1612.03339v1","created_at":"2026-05-18T00:55:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03339","created_at":"2026-05-18T00:55:19Z"},{"alias_kind":"pith_short_12","alias_value":"ERBMLMDYZZT6","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"ERBMLMDYZZT6ONRW","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"ERBMLMDY","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ERBMLMDYZZT6ONRWPH5ECVIN7J","target":"record","payload":{"canonical_record":{"source":{"id":"1612.03339","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-10T20:36:09Z","cross_cats_sorted":[],"title_canon_sha256":"07b5ee52d066c6cf8ea090f453b8da20db626b5b2e833ecf837d9623ae16c120","abstract_canon_sha256":"c5beb941f79592b3aaddd1c1194848f3c265aebc40b530be5cae3f0d6d663e75"},"schema_version":"1.0"},"canonical_sha256":"2442c5b078ce67e7363679fa41550dfa4f88ad53cf3fe4dab5ba5ed5d497717c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:19.549907Z","signature_b64":"7/0D/lFRaNzWb9DGBBUTZVnjCefg0KQkc5A8FH41jypczzUBPp68ugUqUEOmMEEcEfcPCfYF7uKs6YxNWmtqCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2442c5b078ce67e7363679fa41550dfa4f88ad53cf3fe4dab5ba5ed5d497717c","last_reissued_at":"2026-05-18T00:55:19.549350Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:19.549350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.03339","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":"2026-05-18T00:55:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"26KuW+7u4lZG3uI86adYkFGonGYSjLFTRmtil0ovgQSKlKk37zlaAfWvpvD0k2QfHeoeoGt6XrSisuebs6AoAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:40:40.266507Z"},"content_sha256":"93a4b69ec87a4b77cacfc5f15409c5f6548bae86d77aead3be16c0ae595c9003","schema_version":"1.0","event_id":"sha256:93a4b69ec87a4b77cacfc5f15409c5f6548bae86d77aead3be16c0ae595c9003"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ERBMLMDYZZT6ONRWPH5ECVIN7J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Primal-Dual Approximation Algorithm for Min-Sum Single-Machine Scheduling Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"David B. Shmoys, Jos\\'e Verschae, Juli\\'an Mestre, Maurice Cheung","submitted_at":"2016-12-10T20:36:09Z","abstract_excerpt":"We consider the following single-machine scheduling problem, which is often denoted $1||\\sum f_{j}$: we are given $n$ jobs to be scheduled on a single machine, where each job $j$ has an integral processing time $p_j$, and there is a nondecreasing, nonnegative cost function $f_j(C_{j})$ that specifies the cost of finishing $j$ at time $C_{j}$; the objective is to minimize $\\sum_{j=1}^n f_j(C_j)$. Bansal \\& Pruhs recently gave the first constant approximation algorithm with a performance guarantee of 16. We improve on this result by giving a primal-dual pseudo-polynomial-time algorithm based on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03339","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":"2026-05-18T00:55:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aww06cwIBHWzR7o7nBfcgu5bZHdfIZaFTEeC2O5dJekmROxnMFswTRv3TjHySdHwoFh7ZwFpfloPsdc3NwDvAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:40:40.266853Z"},"content_sha256":"95ed64e1723bccd9e81d1b0f1c71c327ec086d8b40c7c02811789e46efff992d","schema_version":"1.0","event_id":"sha256:95ed64e1723bccd9e81d1b0f1c71c327ec086d8b40c7c02811789e46efff992d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ERBMLMDYZZT6ONRWPH5ECVIN7J/bundle.json","state_url":"https://pith.science/pith/ERBMLMDYZZT6ONRWPH5ECVIN7J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ERBMLMDYZZT6ONRWPH5ECVIN7J/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":"2026-06-03T02:40:40Z","links":{"resolver":"https://pith.science/pith/ERBMLMDYZZT6ONRWPH5ECVIN7J","bundle":"https://pith.science/pith/ERBMLMDYZZT6ONRWPH5ECVIN7J/bundle.json","state":"https://pith.science/pith/ERBMLMDYZZT6ONRWPH5ECVIN7J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ERBMLMDYZZT6ONRWPH5ECVIN7J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ERBMLMDYZZT6ONRWPH5ECVIN7J","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":"c5beb941f79592b3aaddd1c1194848f3c265aebc40b530be5cae3f0d6d663e75","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-10T20:36:09Z","title_canon_sha256":"07b5ee52d066c6cf8ea090f453b8da20db626b5b2e833ecf837d9623ae16c120"},"schema_version":"1.0","source":{"id":"1612.03339","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.03339","created_at":"2026-05-18T00:55:19Z"},{"alias_kind":"arxiv_version","alias_value":"1612.03339v1","created_at":"2026-05-18T00:55:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03339","created_at":"2026-05-18T00:55:19Z"},{"alias_kind":"pith_short_12","alias_value":"ERBMLMDYZZT6","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"ERBMLMDYZZT6ONRW","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"ERBMLMDY","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:95ed64e1723bccd9e81d1b0f1c71c327ec086d8b40c7c02811789e46efff992d","target":"graph","created_at":"2026-05-18T00:55:19Z","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":"We consider the following single-machine scheduling problem, which is often denoted $1||\\sum f_{j}$: we are given $n$ jobs to be scheduled on a single machine, where each job $j$ has an integral processing time $p_j$, and there is a nondecreasing, nonnegative cost function $f_j(C_{j})$ that specifies the cost of finishing $j$ at time $C_{j}$; the objective is to minimize $\\sum_{j=1}^n f_j(C_j)$. Bansal \\& Pruhs recently gave the first constant approximation algorithm with a performance guarantee of 16. We improve on this result by giving a primal-dual pseudo-polynomial-time algorithm based on ","authors_text":"David B. Shmoys, Jos\\'e Verschae, Juli\\'an Mestre, Maurice Cheung","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-10T20:36:09Z","title":"A Primal-Dual Approximation Algorithm for Min-Sum Single-Machine Scheduling Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03339","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":"sha256:93a4b69ec87a4b77cacfc5f15409c5f6548bae86d77aead3be16c0ae595c9003","target":"record","created_at":"2026-05-18T00:55:19Z","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":"c5beb941f79592b3aaddd1c1194848f3c265aebc40b530be5cae3f0d6d663e75","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-10T20:36:09Z","title_canon_sha256":"07b5ee52d066c6cf8ea090f453b8da20db626b5b2e833ecf837d9623ae16c120"},"schema_version":"1.0","source":{"id":"1612.03339","kind":"arxiv","version":1}},"canonical_sha256":"2442c5b078ce67e7363679fa41550dfa4f88ad53cf3fe4dab5ba5ed5d497717c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2442c5b078ce67e7363679fa41550dfa4f88ad53cf3fe4dab5ba5ed5d497717c","first_computed_at":"2026-05-18T00:55:19.549350Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:19.549350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7/0D/lFRaNzWb9DGBBUTZVnjCefg0KQkc5A8FH41jypczzUBPp68ugUqUEOmMEEcEfcPCfYF7uKs6YxNWmtqCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:19.549907Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.03339","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93a4b69ec87a4b77cacfc5f15409c5f6548bae86d77aead3be16c0ae595c9003","sha256:95ed64e1723bccd9e81d1b0f1c71c327ec086d8b40c7c02811789e46efff992d"],"state_sha256":"78442fcf853fa7e7903c7b17d4bb7dd667649d52641ef396f98e35fb1725a8c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CDAFekVESKh8SSL2Arquffx4tcZMSIzICKC1H6S75EoW5DZzk4NRlQlbdkaQO+vpANKpAjUwvTYAV/CLnpz1CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T02:40:40.268802Z","bundle_sha256":"60730feb34734bb8c79c9b09fbd6863bc7c83e713193fbe6a1ed0e3bdadb7739"}}