Single machine controllable scheduling with bounded makespan
Bibliographic record
Abstract
In a controllable scheduling environment, the processing time of a job can be shortened by allocating extra resource at a cost, or the job can be declined for processing by paying a penalty. We investigate the single machine controllable scheduling to minimize the sum of the total resource consumption cost, the total job rejection cost, and the makespan of the accepted jobs, where the makespan is upper bounded and the job processing time is a decreasing linear function in the amount of allocated resource. We first show that the studied problem is polynomial solvable if the makespan is unbounded, but otherwise is NP-hard, and characterize important structural properties for the optimal solution; we then take advantage of the structural properties to design several algorithms for the problem, including a pseudo-polynomial time dynamic programming exact algorithm, an O ( n 2 )-time n -approximation algorithm where n is the number of jobs, and building on top of the dynamic programming exact algorithm, the n -approximation algorithm and the bound improvement procedure, two fully polynomial time approximation schemes.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".