{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:56EDNZTENEHRZBQYJQTY4OZ65H","short_pith_number":"pith:56EDNZTE","canonical_record":{"source":{"id":"1701.07242","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-01-25T10:24:44Z","cross_cats_sorted":[],"title_canon_sha256":"257cda72257ffdc16eb6d1e18f27fd15ef69428ba086c7de90affb6afdeac534","abstract_canon_sha256":"e94261d82ec5dbf9e1838613160894e430b33573800c87901e8abd6d5fe247ad"},"schema_version":"1.0"},"canonical_sha256":"ef8836e664690f1c86184c278e3b3ee9f91bf8ef8a28eda1f725247f653697b0","source":{"kind":"arxiv","id":"1701.07242","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.07242","created_at":"2026-05-18T00:52:07Z"},{"alias_kind":"arxiv_version","alias_value":"1701.07242v1","created_at":"2026-05-18T00:52:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.07242","created_at":"2026-05-18T00:52:07Z"},{"alias_kind":"pith_short_12","alias_value":"56EDNZTENEHR","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"56EDNZTENEHRZBQY","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"56EDNZTE","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:56EDNZTENEHRZBQYJQTY4OZ65H","target":"record","payload":{"canonical_record":{"source":{"id":"1701.07242","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-01-25T10:24:44Z","cross_cats_sorted":[],"title_canon_sha256":"257cda72257ffdc16eb6d1e18f27fd15ef69428ba086c7de90affb6afdeac534","abstract_canon_sha256":"e94261d82ec5dbf9e1838613160894e430b33573800c87901e8abd6d5fe247ad"},"schema_version":"1.0"},"canonical_sha256":"ef8836e664690f1c86184c278e3b3ee9f91bf8ef8a28eda1f725247f653697b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:07.065334Z","signature_b64":"LDksYdBDkg8NpVbcq3fXxjWB5h4Wg2b2ZulY1mAJozGQhBHGRX6hdniJ3Dm66sjrC8OvHU/YoTYmnZGOcSg1AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef8836e664690f1c86184c278e3b3ee9f91bf8ef8a28eda1f725247f653697b0","last_reissued_at":"2026-05-18T00:52:07.064711Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:07.064711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.07242","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":"2026-05-18T00:52:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e2S/A+wz0oFumWwMTrhzlkfiI46p3D6lSVAtNDPteCOjRCBKGHtt6BPhy9NxAXR4Ov1on7wNrpPcJw9ngM9rBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:16:10.153619Z"},"content_sha256":"1c49582bb97b87bba5867ba75eda1f32c0cf5bacf61c3783e37ac1bfce5ea13c","schema_version":"1.0","event_id":"sha256:1c49582bb97b87bba5867ba75eda1f32c0cf5bacf61c3783e37ac1bfce5ea13c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:56EDNZTENEHRZBQYJQTY4OZ65H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Structural Parameters for Scheduling with Assignment Restrictions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Klaus Jansen, Marten Maack, Roberto Solis-Oba","submitted_at":"2017-01-25T10:24:44Z","abstract_excerpt":"We consider scheduling on identical and unrelated parallel machines with job assignment restrictions. These problems are NP-hard and they do not admit polynomial time approximation algorithms with approximation ratios smaller than $1.5$ unless P$=$NP. However, if we impose limitations on the set of machines that can process a job, the problem sometimes becomes easier in the sense that algorithms with approximation ratios better than $1.5$ exist. We introduce three graphs, based on the assignment restrictions and study the computational complexity of the scheduling problem with respect to struc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07242","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":"2026-05-18T00:52:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dFpaHe/WNgjT1RrHdFlOrxMKW9qbJ7AiEs+kuuVUZYaTErhw95vyw7OnBzoRtk2L7YlV8xsZjmRgsjbGL8HNDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:16:10.154290Z"},"content_sha256":"d092682896ab4c60c1cb86f2d234fad045f8708c9198e638922e1c729e0c0d53","schema_version":"1.0","event_id":"sha256:d092682896ab4c60c1cb86f2d234fad045f8708c9198e638922e1c729e0c0d53"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/56EDNZTENEHRZBQYJQTY4OZ65H/bundle.json","state_url":"https://pith.science/pith/56EDNZTENEHRZBQYJQTY4OZ65H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/56EDNZTENEHRZBQYJQTY4OZ65H/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":"2026-05-28T22:16:10Z","links":{"resolver":"https://pith.science/pith/56EDNZTENEHRZBQYJQTY4OZ65H","bundle":"https://pith.science/pith/56EDNZTENEHRZBQYJQTY4OZ65H/bundle.json","state":"https://pith.science/pith/56EDNZTENEHRZBQYJQTY4OZ65H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/56EDNZTENEHRZBQYJQTY4OZ65H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:56EDNZTENEHRZBQYJQTY4OZ65H","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":"e94261d82ec5dbf9e1838613160894e430b33573800c87901e8abd6d5fe247ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-01-25T10:24:44Z","title_canon_sha256":"257cda72257ffdc16eb6d1e18f27fd15ef69428ba086c7de90affb6afdeac534"},"schema_version":"1.0","source":{"id":"1701.07242","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.07242","created_at":"2026-05-18T00:52:07Z"},{"alias_kind":"arxiv_version","alias_value":"1701.07242v1","created_at":"2026-05-18T00:52:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.07242","created_at":"2026-05-18T00:52:07Z"},{"alias_kind":"pith_short_12","alias_value":"56EDNZTENEHR","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"56EDNZTENEHRZBQY","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"56EDNZTE","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:d092682896ab4c60c1cb86f2d234fad045f8708c9198e638922e1c729e0c0d53","target":"graph","created_at":"2026-05-18T00:52:07Z","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 scheduling on identical and unrelated parallel machines with job assignment restrictions. These problems are NP-hard and they do not admit polynomial time approximation algorithms with approximation ratios smaller than $1.5$ unless P$=$NP. However, if we impose limitations on the set of machines that can process a job, the problem sometimes becomes easier in the sense that algorithms with approximation ratios better than $1.5$ exist. We introduce three graphs, based on the assignment restrictions and study the computational complexity of the scheduling problem with respect to struc","authors_text":"Klaus Jansen, Marten Maack, Roberto Solis-Oba","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-01-25T10:24:44Z","title":"Structural Parameters for Scheduling with Assignment Restrictions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07242","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":"sha256:1c49582bb97b87bba5867ba75eda1f32c0cf5bacf61c3783e37ac1bfce5ea13c","target":"record","created_at":"2026-05-18T00:52:07Z","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":"e94261d82ec5dbf9e1838613160894e430b33573800c87901e8abd6d5fe247ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-01-25T10:24:44Z","title_canon_sha256":"257cda72257ffdc16eb6d1e18f27fd15ef69428ba086c7de90affb6afdeac534"},"schema_version":"1.0","source":{"id":"1701.07242","kind":"arxiv","version":1}},"canonical_sha256":"ef8836e664690f1c86184c278e3b3ee9f91bf8ef8a28eda1f725247f653697b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef8836e664690f1c86184c278e3b3ee9f91bf8ef8a28eda1f725247f653697b0","first_computed_at":"2026-05-18T00:52:07.064711Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:07.064711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LDksYdBDkg8NpVbcq3fXxjWB5h4Wg2b2ZulY1mAJozGQhBHGRX6hdniJ3Dm66sjrC8OvHU/YoTYmnZGOcSg1AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:07.065334Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.07242","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c49582bb97b87bba5867ba75eda1f32c0cf5bacf61c3783e37ac1bfce5ea13c","sha256:d092682896ab4c60c1cb86f2d234fad045f8708c9198e638922e1c729e0c0d53"],"state_sha256":"a01fd10e76465496c3c337887280a17704f4b2c50d742be25b762a0cdba8d13a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GKcwbibhw9F5XTC0q9mSzwwHQSWNi0u1nXvWovOZEAe0nuoSooYvR0Y6mwhy72aAO0U+bJz3XN/FcCCVs+KXBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:16:10.157917Z","bundle_sha256":"742b10a1956a08e5032e598a2633969f000718502321d29a94774b8f27ce8960"}}