{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:35ABWQHDO3I262JS2BOWOXDO4T","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":"883fdd86e688b898efa5b376b7577fa8cd7b84c4967576b0acdcb09ee86fce9b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-27T13:21:26Z","title_canon_sha256":"c0cf1c912ea1882852e1ee6522008e078373963697decd1450c7f4237712b901"},"schema_version":"1.0","source":{"id":"1507.07396","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.07396","created_at":"2026-05-18T01:31:13Z"},{"alias_kind":"arxiv_version","alias_value":"1507.07396v3","created_at":"2026-05-18T01:31:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07396","created_at":"2026-05-18T01:31:13Z"},{"alias_kind":"pith_short_12","alias_value":"35ABWQHDO3I2","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"35ABWQHDO3I262JS","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"35ABWQHD","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:8bffde5092a43873a4d1a553a9768471b3e3fa2d05a230950e54670bdc9deb20","target":"graph","created_at":"2026-05-18T01:31:13Z","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":"Makespan minimization in restricted assignment $(R|p_{ij}\\in \\{p_j, \\infty\\}|C_{\\max})$ is a classical problem in the field of machine scheduling. In a landmark paper in 1990 [8], Lenstra, Shmoys, and Tardos gave a 2-approximation algorithm and proved that the problem cannot be approximated within 1.5 unless P=NP. The upper and lower bounds of the problem have been essentially unimproved in the intervening 25 years, despite several remarkable successful attempts in some special cases of the problem [2,4,12] recently.\n  In this paper, we consider a special case called graph-balancing with light","authors_text":"Chien-Chung Huang, Sebastian Ott","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-27T13:21:26Z","title":"A Combinatorial Approximation Algorithm for Graph Balancing with Light Hyper Edges"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07396","kind":"arxiv","version":3},"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":"sha256:8ec4e5f723c2284c678a4076b48836b0384405f32b3a548f5d0aa2f49e42db35","target":"record","created_at":"2026-05-18T01:31:13Z","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":"883fdd86e688b898efa5b376b7577fa8cd7b84c4967576b0acdcb09ee86fce9b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-27T13:21:26Z","title_canon_sha256":"c0cf1c912ea1882852e1ee6522008e078373963697decd1450c7f4237712b901"},"schema_version":"1.0","source":{"id":"1507.07396","kind":"arxiv","version":3}},"canonical_sha256":"df401b40e376d1af6932d05d675c6ee4f6918692997b89ace191cf016559f389","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df401b40e376d1af6932d05d675c6ee4f6918692997b89ace191cf016559f389","first_computed_at":"2026-05-18T01:31:13.467344Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:13.467344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p3aiYGoBOun0GZS1LeqY+nbGPOtZVrmnuTuDTpIxXqb61WSfrzeW3O3A3SO22F8uVwC8tK98epKpz0TDLXe5BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:13.467880Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.07396","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ec4e5f723c2284c678a4076b48836b0384405f32b3a548f5d0aa2f49e42db35","sha256:8bffde5092a43873a4d1a553a9768471b3e3fa2d05a230950e54670bdc9deb20"],"state_sha256":"7c08676bed4aff9f8028c8bcc0760b9bfc30f3a4e4ce1334259ceb03688fec04"}