On preemption redundancy in scheduling unit processing time jobs on two parallel machines
Bibliographic record
Abstract
McNaughton’s theorem (1959) states that preemptions in scheduling arbitrary processing time jobs on identical parallel machines to minimize the total weighted completion time are redundant. Du, Leung and Young (1991) proved that this remains true even though the jobs have precedence constraints in the form of chains. There are known simple counterexamples showing that other extensions of McNaughton’s theorem to other criteria or more general precedence constraints such as intrees or outtrees, or different release dates of jobs, or different speeds of machines, are not true even for equal weights of jobs. In this paper we show that in the case of two machines and unit processing times, preemptions are still advantageous for intrees or machines with different speeds even for equal weights, or outtrees for different weights, but become redundant for outtrees and equal weights even for different release dates. We also conjecture that the latter statement is actually true for any number of machines.
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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 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".