{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:43FBMTCMNUAH5YTANWPWADYWCN","short_pith_number":"pith:43FBMTCM","canonical_record":{"source":{"id":"1606.08817","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-06-28T18:31:00Z","cross_cats_sorted":[],"title_canon_sha256":"7486bd43c01b566e2cbc83e1b51036aa1d5e5b9b0e24dae8c209c0ec80cffb2f","abstract_canon_sha256":"fd7d0b9738475ae13618f613a88615bbaf0fcc149f9bbd36b0795044af940dbf"},"schema_version":"1.0"},"canonical_sha256":"e6ca164c4c6d007ee2606d9f600f161368a4514e17175947a4ada61c4eec79ca","source":{"kind":"arxiv","id":"1606.08817","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.08817","created_at":"2026-05-18T01:11:47Z"},{"alias_kind":"arxiv_version","alias_value":"1606.08817v1","created_at":"2026-05-18T01:11:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.08817","created_at":"2026-05-18T01:11:47Z"},{"alias_kind":"pith_short_12","alias_value":"43FBMTCMNUAH","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"43FBMTCMNUAH5YTA","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"43FBMTCM","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:43FBMTCMNUAH5YTANWPWADYWCN","target":"record","payload":{"canonical_record":{"source":{"id":"1606.08817","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-06-28T18:31:00Z","cross_cats_sorted":[],"title_canon_sha256":"7486bd43c01b566e2cbc83e1b51036aa1d5e5b9b0e24dae8c209c0ec80cffb2f","abstract_canon_sha256":"fd7d0b9738475ae13618f613a88615bbaf0fcc149f9bbd36b0795044af940dbf"},"schema_version":"1.0"},"canonical_sha256":"e6ca164c4c6d007ee2606d9f600f161368a4514e17175947a4ada61c4eec79ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:47.082558Z","signature_b64":"Njq+zzAPWboc31YQxznRB/4ruygwdbO/zsDXNe2rNJ5Sb/MYphuXRRBBoEhnOU7mQDJis79GaDLl3SaUvEggDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6ca164c4c6d007ee2606d9f600f161368a4514e17175947a4ada61c4eec79ca","last_reissued_at":"2026-05-18T01:11:47.082177Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:47.082177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.08817","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":"2026-05-18T01:11:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+MuMPvnYcvHtIRGKYFgal785aURot9rhfOgX0Dn4xuHtLzQ2FQWJ3WxmkJjDlv58rUEL1C+PAD0XE+jdVJuoDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:56:08.589620Z"},"content_sha256":"9d09c21f09b8684efda4fdf43b4798001457eb3b1dbac97ff006898118e197ec","schema_version":"1.0","event_id":"sha256:9d09c21f09b8684efda4fdf43b4798001457eb3b1dbac97ff006898118e197ec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:43FBMTCMNUAH5YTANWPWADYWCN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Better Unrelated Machine Scheduling for Weighted Completion Time via Random Offsets from Non-Uniform Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Shi Li, Sungjin Im","submitted_at":"2016-06-28T18:31:00Z","abstract_excerpt":"In this paper we consider the classic scheduling problem of minimizing total weighted completion time on unrelated machines when jobs have release times, i.e, $R | r_{ij} | \\sum_j w_j C_j$ using the three-field notation. For this problem, a 2-approximation is known based on a novel convex programming (J. ACM 2001 by Skutella). It has been a long standing open problem if one can improve upon this 2-approximation (Open Problem 8 in J. of Sched. 1999 by Schuurman and Woeginger). We answer this question in the affirmative by giving a 1.8786-approximation. We achieve this via a surprisingly simple "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08817","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":"2026-05-18T01:11:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7ot2rIa+Xa7gAtt7HCQYFZYme9wE0yt6xuzaWH6a3B70JhV9/vvqFVXNHo5jFwKdDSuJXb+8EvoadfIL6YSBBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:56:08.589950Z"},"content_sha256":"0f23ae577c15d3e556750e8e586e142edcd0b0abfad1e9775db7f409f6706a25","schema_version":"1.0","event_id":"sha256:0f23ae577c15d3e556750e8e586e142edcd0b0abfad1e9775db7f409f6706a25"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/43FBMTCMNUAH5YTANWPWADYWCN/bundle.json","state_url":"https://pith.science/pith/43FBMTCMNUAH5YTANWPWADYWCN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/43FBMTCMNUAH5YTANWPWADYWCN/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":"2026-06-27T12:56:08Z","links":{"resolver":"https://pith.science/pith/43FBMTCMNUAH5YTANWPWADYWCN","bundle":"https://pith.science/pith/43FBMTCMNUAH5YTANWPWADYWCN/bundle.json","state":"https://pith.science/pith/43FBMTCMNUAH5YTANWPWADYWCN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/43FBMTCMNUAH5YTANWPWADYWCN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:43FBMTCMNUAH5YTANWPWADYWCN","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":"fd7d0b9738475ae13618f613a88615bbaf0fcc149f9bbd36b0795044af940dbf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-06-28T18:31:00Z","title_canon_sha256":"7486bd43c01b566e2cbc83e1b51036aa1d5e5b9b0e24dae8c209c0ec80cffb2f"},"schema_version":"1.0","source":{"id":"1606.08817","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.08817","created_at":"2026-05-18T01:11:47Z"},{"alias_kind":"arxiv_version","alias_value":"1606.08817v1","created_at":"2026-05-18T01:11:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.08817","created_at":"2026-05-18T01:11:47Z"},{"alias_kind":"pith_short_12","alias_value":"43FBMTCMNUAH","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"43FBMTCMNUAH5YTA","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"43FBMTCM","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:0f23ae577c15d3e556750e8e586e142edcd0b0abfad1e9775db7f409f6706a25","target":"graph","created_at":"2026-05-18T01:11:47Z","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":"In this paper we consider the classic scheduling problem of minimizing total weighted completion time on unrelated machines when jobs have release times, i.e, $R | r_{ij} | \\sum_j w_j C_j$ using the three-field notation. For this problem, a 2-approximation is known based on a novel convex programming (J. ACM 2001 by Skutella). It has been a long standing open problem if one can improve upon this 2-approximation (Open Problem 8 in J. of Sched. 1999 by Schuurman and Woeginger). We answer this question in the affirmative by giving a 1.8786-approximation. We achieve this via a surprisingly simple ","authors_text":"Shi Li, Sungjin Im","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-06-28T18:31:00Z","title":"Better Unrelated Machine Scheduling for Weighted Completion Time via Random Offsets from Non-Uniform Distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08817","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":"sha256:9d09c21f09b8684efda4fdf43b4798001457eb3b1dbac97ff006898118e197ec","target":"record","created_at":"2026-05-18T01:11:47Z","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":"fd7d0b9738475ae13618f613a88615bbaf0fcc149f9bbd36b0795044af940dbf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-06-28T18:31:00Z","title_canon_sha256":"7486bd43c01b566e2cbc83e1b51036aa1d5e5b9b0e24dae8c209c0ec80cffb2f"},"schema_version":"1.0","source":{"id":"1606.08817","kind":"arxiv","version":1}},"canonical_sha256":"e6ca164c4c6d007ee2606d9f600f161368a4514e17175947a4ada61c4eec79ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6ca164c4c6d007ee2606d9f600f161368a4514e17175947a4ada61c4eec79ca","first_computed_at":"2026-05-18T01:11:47.082177Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:47.082177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Njq+zzAPWboc31YQxznRB/4ruygwdbO/zsDXNe2rNJ5Sb/MYphuXRRBBoEhnOU7mQDJis79GaDLl3SaUvEggDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:47.082558Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.08817","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d09c21f09b8684efda4fdf43b4798001457eb3b1dbac97ff006898118e197ec","sha256:0f23ae577c15d3e556750e8e586e142edcd0b0abfad1e9775db7f409f6706a25"],"state_sha256":"1b192f5c2de9664e8e91d6f6b1a3ffe34b297ee8005f7dd8ea95db390151c848"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wpnLApSL1U0OkeOIhPOQeBubDZP0qzA+aLceZMtmq/6SIaQBIMEQh/UjAFuQ3nEBAMux9uqGUs80XSpq51tuAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T12:56:08.591853Z","bundle_sha256":"188e4949362b9781926813e9504ce8fc1798a5066648a32c785f080f0b2d4186"}}