Most Popular Package Design and NP-Hard Problem
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Given a set of items, and a set of user preferences, we investigate the problem of designing a most popular package (or say, a pattern), i.e., a subset of items that maximizes the number of satisfied users. It is a typical problem of data mining. In this paper, we address this issue and propose an efficient algorithm for solving the problem based on a graph structure, called a p*-graph, used to represent the preference of a user, by which a lot of useless checks can be avoided. The time complexity of the algorithm is bounded by O(n2m3), where m is the number of items (or say, attributes) and n is the number of user preferences. Since the problem is essentially NP-hard, the algorithm discussed in this chapter in fact provides a proof of P = NP . CCS Concepts: \(\bullet\) Theory of computation \(\to\) Minimum satisfiability problem.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.006 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.011 | 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