{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:35ABWQHDO3I262JS2BOWOXDO4T","short_pith_number":"pith:35ABWQHD","canonical_record":{"source":{"id":"1507.07396","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-27T13:21:26Z","cross_cats_sorted":[],"title_canon_sha256":"c0cf1c912ea1882852e1ee6522008e078373963697decd1450c7f4237712b901","abstract_canon_sha256":"883fdd86e688b898efa5b376b7577fa8cd7b84c4967576b0acdcb09ee86fce9b"},"schema_version":"1.0"},"canonical_sha256":"df401b40e376d1af6932d05d675c6ee4f6918692997b89ace191cf016559f389","source":{"kind":"arxiv","id":"1507.07396","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:35ABWQHDO3I262JS2BOWOXDO4T","target":"record","payload":{"canonical_record":{"source":{"id":"1507.07396","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-27T13:21:26Z","cross_cats_sorted":[],"title_canon_sha256":"c0cf1c912ea1882852e1ee6522008e078373963697decd1450c7f4237712b901","abstract_canon_sha256":"883fdd86e688b898efa5b376b7577fa8cd7b84c4967576b0acdcb09ee86fce9b"},"schema_version":"1.0"},"canonical_sha256":"df401b40e376d1af6932d05d675c6ee4f6918692997b89ace191cf016559f389","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:13.467880Z","signature_b64":"p3aiYGoBOun0GZS1LeqY+nbGPOtZVrmnuTuDTpIxXqb61WSfrzeW3O3A3SO22F8uVwC8tK98epKpz0TDLXe5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df401b40e376d1af6932d05d675c6ee4f6918692997b89ace191cf016559f389","last_reissued_at":"2026-05-18T01:31:13.467344Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:13.467344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.07396","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:31:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LVyNlqWZjeGtFt/6Q3t2SpG7VVrnQMCY+arU4WSKbBR51slRjAqO1ljElOFkzX+nTuQXbj89zUVb0fxpipP8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:19:16.216077Z"},"content_sha256":"8ec4e5f723c2284c678a4076b48836b0384405f32b3a548f5d0aa2f49e42db35","schema_version":"1.0","event_id":"sha256:8ec4e5f723c2284c678a4076b48836b0384405f32b3a548f5d0aa2f49e42db35"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:35ABWQHDO3I262JS2BOWOXDO4T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Combinatorial Approximation Algorithm for Graph Balancing with Light Hyper Edges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Chien-Chung Huang, Sebastian Ott","submitted_at":"2015-07-27T13:21:26Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07396","kind":"arxiv","version":3},"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":"2026-05-18T01:31:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v4hQW5tNUXFm2eIKRJCFec6Zc1kYYLYoiVZzwHRa1zQPpEnFYtpFHnh+4kSZ3QjE3ecPVJK1VXgdIFvjmYmsCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:19:16.216432Z"},"content_sha256":"8bffde5092a43873a4d1a553a9768471b3e3fa2d05a230950e54670bdc9deb20","schema_version":"1.0","event_id":"sha256:8bffde5092a43873a4d1a553a9768471b3e3fa2d05a230950e54670bdc9deb20"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/35ABWQHDO3I262JS2BOWOXDO4T/bundle.json","state_url":"https://pith.science/pith/35ABWQHDO3I262JS2BOWOXDO4T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/35ABWQHDO3I262JS2BOWOXDO4T/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":"2026-06-24T21:19:16Z","links":{"resolver":"https://pith.science/pith/35ABWQHDO3I262JS2BOWOXDO4T","bundle":"https://pith.science/pith/35ABWQHDO3I262JS2BOWOXDO4T/bundle.json","state":"https://pith.science/pith/35ABWQHDO3I262JS2BOWOXDO4T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/35ABWQHDO3I262JS2BOWOXDO4T/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m7eoytLPzkpP9jGF2E0Sk3Jxf0INbvxl3Fw+CC62SgIrDeJTDhsuweb8HDXolj218DXQEg3WK0f69X5Xf9H4BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T21:19:16.218279Z","bundle_sha256":"72c1a0ca53c89a3c2ed9d6ce3f495770e418ab5362e2d3b705df517ba84fa252"}}