Group Role Assignment With Constraints (GRA+): A New Category of Assignment Problems
Bibliographic record
Abstract
This article systematically establishes a new category of assignment problems by reviewing and extending the problems related to group role assignment (GRA) from a novel vision. After reviewing seven related GRA with Constraints (GRA+) problems, this article specifies three new major assignment problems to make GRA+ problems complete and coherent. In addition, this article proves a series of new related theorems, proposes new conditions for the specified problems to have feasible solutions, and verifies the hardness of the newly specified problems. This article finally verifies the value of the presented theoretical work and provides a generalized formalization of this category of problems, i.e., the one highly abstract optimization problem, which is specified the first time. This article contributes to the literature of assignment problems with a novel category of well-defined problems, i.e., GRA+. The presented problem category is original, consistent, but far from complete. It will initiate further innovations in assignment research along with the presented directions. This article again demonstrates the power of the methodology role-based collaboration (RBC), and the environments—classes, agents, roles, groups, and objects (E-CARGO) model.
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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 | 0.006 | 0.014 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.003 | 0.005 |
| Scholarly communication | 0.005 | 0.013 |
| Open science | 0.003 | 0.006 |
| Research integrity | 0.004 | 0.006 |
| Insufficient payload (model declined to judge) | 0.010 | 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".