Efficient minimization of sum and differential costs on machines with job placement constraints
Bibliographic record
Abstract
We revisit the problem of assigning n jobs to m machines/servers. We study this problem under more general settings, which capture important aspects of applications that arise in networking and information systems. In particular, we consider jobs that have placement constraints and machines that are heterogeneous. The cost incurred at a machine is given by any general convex function on the number of jobs assigned to it. We aim to minimize the sum cost and the maximum differential cost. Through a network-flow equivalence transformation, we observe how these two objectives are fundamentally related, showing that sum-cost minimization implies maximum-differential-cost minimization. We propose an efficient algorithm termed Maximum Edge-Cost Cycle Cancelling (MEC3) to solve the sum-cost minimization problem with O(n2m2) time complexity. Furthermore, for applications where only the maximum differential cost is of concern, we further improve the efficiency of MEC3by proposing an early stop condition. We implement MEC3and two other algorithms from the literature. Using benchmark input instances, we show that MEC3has substantially lower run time than the other algorithms.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 | 0.004 |
| 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 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".