Min-Max Problems on Factor Graphs
Bibliographic record
Abstract
We study the min-max problem in factor graphs, which seeks the assignment that minimizes the maximum value over all factors. We reduce this problem to both min-sum and sum-product infer-ence, and focus on the later. In this approach the min-max inference problem is reduced to a sequence of Constraint Satisfaction Problems (CSP), which allows us to solve the problem by sampling from a uniform distribution over the set of solutions. We demonstrate how this scheme provides a message passing solution to several NP-hard combinatorial problems, such as min-max clustering (a.k.a.K-clustering), asymmetric K-center clustering problem, K-packing and the bottleneck traveling salesman problem. Further-more, we theoretically relate the min-max reduc-tions and several NP hard decision problems such as clique cover, set-cover, maximum clique and Hamiltonian cycle, therefore also providing mes-sage passing solutions for these problems. Ex-perimental results suggest that message passing often provides near optimal min-max solutions for moderate size instances. 1.
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How this classification was reachedexpand
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".