Parameterized Approximation for Capacitated <i>d</i>-Hitting Set with Hard Capacities
Bibliographic record
Abstract
In the CAPACITATED d-HlTTING Set problem input is a universe U equipped with a capacity function cap : U → ℕ, and a collection A of subsets of U, each of size at most d. The task is to find a minimum size subset S of U and an assignment φ : A → S such that, for every set A ∈ A we have φ (Α ) ∈ A and for every x ∈ U we have |φ-1(χ)| ≤ cap(x ). Here φ-1(χ) is the collection of sets in A mapped to x by φ. Such a set S is called a capacitated hitting set. When d = 2 the problem is known under the name CAPACITATED VERTEX COVER. In Weighted Capacitated d-HlTTING Set each element of U has a positive integer weight and the goal is to find a capacitated hitting set of minimum weight.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 | 0.001 | 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".