Approximation Algorithm for Scheduling Parallel Machines with Machine Eligibility Restrictions and special jobs
Bibliographic record
Abstract
This paper addresses the scheduling problem of parallel machines with machine eligibility restrictions and special jobs with the objective of minimizing the makespan. Each job can only be assigned to a specific subset of the machines. And the processing times of jobs are restricted to one of two values, 1 andε. A semi-matching model G=[J∪M,E,W] is presented to formulate this scheduling problem. We propose an approximation algorithm, which is composed of two steps, that is, initial solution construction and initial solution improvement. The initial solution construction algorithm is developed to build a feasible solution by performing a simple greedy heuristic method. The initial solution is used as a starting point by the improvement algorithm. The main idea of the improvement algorithm is to construct alternating tree, then to find the optimal alternating path for each vertex in M iteratively. In order to improve efficiency, the length of each path in alternating tree is limited to 4 at most.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".