{"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"}