{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:3SEPLUB6PGMMZ5GBANMDTOV4M5","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":"0411a4e0acfc45db161ba310b9cdd0f494e87870478f6ae3819cf7a366233b49","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-09-23T07:12:49Z","title_canon_sha256":"245a4cf796fd56634d9c383fb160854841fc7cc7e1f76122aaa8f0cdd91572f6"},"schema_version":"1.0","source":{"id":"1009.4529","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.4529","created_at":"2026-05-18T04:40:30Z"},{"alias_kind":"arxiv_version","alias_value":"1009.4529v1","created_at":"2026-05-18T04:40:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4529","created_at":"2026-05-18T04:40:30Z"},{"alias_kind":"pith_short_12","alias_value":"3SEPLUB6PGMM","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3SEPLUB6PGMMZ5GB","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3SEPLUB6","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:fec18ce15bcd7fc338faa2442e2d29227728cdf8fa007862614a40e00c206a22","target":"graph","created_at":"2026-05-18T04:40:30Z","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":"Scheduling with assignment restrictions is an important special case of scheduling unrelated machines which has attracted much attention in the recent past. While a lower bound on approximability of 3/2 is known for its most general setting, subclasses of the problem admit polynomial-time approximation schemes. This note provides a PTAS for tree-like hierarchical structures, improving on a recent 4/3-approximation by Huo and Leung.","authors_text":"Ulrich M. Schwarz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-09-23T07:12:49Z","title":"A PTAS for Scheduling with Tree Assignment Restrictions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4529","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:e1dd5fc992b4ff237d8b802973f0a0226ef695395337afda96bac3f99057a96c","target":"record","created_at":"2026-05-18T04:40:30Z","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":"0411a4e0acfc45db161ba310b9cdd0f494e87870478f6ae3819cf7a366233b49","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-09-23T07:12:49Z","title_canon_sha256":"245a4cf796fd56634d9c383fb160854841fc7cc7e1f76122aaa8f0cdd91572f6"},"schema_version":"1.0","source":{"id":"1009.4529","kind":"arxiv","version":1}},"canonical_sha256":"dc88f5d03e7998ccf4c1035839babc676ff6136f7e611bac122404eac32a2311","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc88f5d03e7998ccf4c1035839babc676ff6136f7e611bac122404eac32a2311","first_computed_at":"2026-05-18T04:40:30.216248Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:30.216248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SGJ5ekr2QKMdMn0JdsPpWq0hUMTbzciNXUb701w3wRtY+p/pJ39SoZheaFndkEWO8AywhnrSDHfYoBSMgRzmAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:30.216967Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.4529","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1dd5fc992b4ff237d8b802973f0a0226ef695395337afda96bac3f99057a96c","sha256:fec18ce15bcd7fc338faa2442e2d29227728cdf8fa007862614a40e00c206a22"],"state_sha256":"f40781fe5e417cb9dafe30f09fd5fb618224c4d0a03403b294d1293217494ce0"}