Bibliographic record
Abstract
In earlier versions of the community discovering problem, the overlap between communities was restricted by a simple count upper-bound. In this paper, we introduce the [Formula: see text]-Packing with [Formula: see text]-Overlap problem to allow for more complex constraints in the overlap region than those previously studied. Let [Formula: see text] be all possible subsets of vertices of [Formula: see text] each of size at most [Formula: see text], and [Formula: see text] be a function. The [Formula: see text]-Packing with [Formula: see text]-Overlap problem seeks at least [Formula: see text] induced subgraphs in a graph [Formula: see text] subject to: (i) each subgraph has at most [Formula: see text] vertices and obeys a property [Formula: see text], and (ii) for any pair [Formula: see text], with [Formula: see text], [Formula: see text] (i.e., the pair [Formula: see text] does not conflict). We also consider a variant that arises in clustering applications: each subgraph of a solution must contain a set of vertices from a given collection of sets [Formula: see text], and no pair of subgraphs may share vertices from the sets of [Formula: see text]. In addition, we propose similar formulations for packing hypergraphs. We give an [Formula: see text] algorithm for our problems where [Formula: see text] is the parameter and [Formula: see text] and [Formula: see text] are constants, provided that: (i) [Formula: see text] is computable in polynomial time in [Formula: see text] and (ii) the function [Formula: see text] satisfies specific conditions. Specifically, [Formula: see text] is hereditary, applicable only to overlapping subgraphs, and computable in polynomial time in [Formula: see text] and [Formula: see text]. Motivated by practical applications we give several examples of [Formula: see text] functions which meet those conditions.
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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 | 0.003 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.009 | 0.003 |
| Research integrity | 0.000 | 0.001 |
| 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".