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We study structure of potential minimal counterexamples to this conjecture and prove that the conjecture holds for the cases (i) n > 5m, (ii) m = 2, (iii) m = 3, and (iv) m greater than or equal to 4, n less than or equal to 3m, where n is the number of jobs. We further conclude that to verify the conject"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1312.3345","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-12-11T21:07:58Z","cross_cats_sorted":["cs.DM","math.CO","math.OC"],"title_canon_sha256":"15decb51ecb2ef6ccffc4d4f494581d99ccafc3c8e37cd5c21cb031dba979540","abstract_canon_sha256":"d838bd729720a60c34e9414d7a56bd7cb78288bc09384a401a842a926405ab00"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:23.697681Z","signature_b64":"6VDzc03yiRgrJE39ICdFGdkdJM97uD6DfrFgA3AE4srmy3qcrEj/BlvCDDgx6VkT5Fd5MJWNE6IvLSQKHn1yDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"676a962f27fba1392d9922e1efbbbb9eca886cc563834913c2fb04dde5bef8e7","last_reissued_at":"2026-05-18T03:04:23.697213Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:23.697213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Worst-Case Performance Analysis of Some Approximation Algorithms for Minimizing Makespan and Flow-Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO","math.OC"],"primary_cat":"cs.DS","authors_text":"Levent Tuncel, Michael Huang, Peruvemba Sundaram Ravi","submitted_at":"2013-12-11T21:07:58Z","abstract_excerpt":"In 1976, Coffman and Sethi conjectured that a natural extension of LPT list scheduling to the bicriteria scheduling problem of minimizing makespan over flowtime optimal schedules, called LD algorithm, has a simple worst-case performance bound: (5m-2)/(4m-1), where m is the number of machines. 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