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 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 | 0.015 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.004 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.007 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.011 | 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".