{"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. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3345","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"}