New and improved algorithms for minsum shop scheduling
Bibliographic record
Abstract
We consider a general class of multiprocessor shop scheduling problems with a minsum objective, and present approximation methods based on linear programming relaxations in the operation completion times. These LP relaxations use new classes of valid inequalities for multistage jobs. We first consider open shop problems with total weighted job completion time objective. For the nonpreemptive problem Ojj P w j C j , we introduce "LP-based precedence constraints" and derive a 5.83-approximation algorithm. For its preemptive version, Ojpmtnj P w j C j , we show that a simple job-based greedy algorithm, using directly the LP solution, yields a 3approximation. We then consider a general class of multiprocessor shop scheduling problems, preemptive or nonpreemptive, with precedence constraints between operations, with job or operation release dates, and with a general minsum objective. This class of objectives includes, among others, weighted sums of operations completion times, job comp...
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.008 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".