Constructive algorithms for the partial directed weighted improper coloring problem
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Bibliographic record
Abstract
Given a complete directed graph G with weights on the vertices and on the arcs, a θ-improper k-coloring is an assignment of at most k different colors to the vertices of G such that the weight of every vertex v is greater, by a given factor 1/θ, than the sum of the weights on the arcs (u,v) entering v with the tail u of the same color as v. For a given real number θ and an integer k, the Partial Directed Weigthed Improper Coloring Problem (PDWICP) is to determine the order of the largest induced subgraph G′ of G such that G′ admits a θ-improper k-coloring. This problem is motivated by a practical channel assignment application where the objective is to maximize the number of simultaneously communicating mobiles in a wireless network. We consider three constructive algorithms for the standard vertex coloring problem, and adapt them to the PDWICP. We show that they perform better than today's phone operator systems based on decentralized channel assignment strategies such as fractional frequency reuse.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| 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 it