Generalizing contexts amenable to greedy and greedy-like algorithms
Bibliographic record
Abstract
One central question in theoretical computer science is how to solve problems accurately and quickly. Despite the encouraging development of various algorithmic techniques in the past, we are still at the very beginning of the understanding of these techniques. One particularly interesting paradigm is the greedy algorithm paradigm. Informally, a greedy algorithm builds a solution to a problem incrementally by making locally optimal decisions at each step. Greedy algorithms are important in algorithmdesign as they are natural, conceptually simple to state and usually efficient. Despite wide applications of greedy algorithms in practice, their behaviour is notwell understood. However,we do knowthat in several specific settings, greedy algorithms can achieve good results. This thesis focuses on examining contexts in which greedy and greedy-like algorithms are successful, and extending them to more general settings. In particular, we investigate structural properties of graphs and set systems, families of special functions, and greedy approximation algorithms for several classic NP-hard problems in those contexts. A natural phenomenon we observe is a trade-off between the approximation ratio and the generality of those contexts.
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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 | 0.002 | 0.016 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.005 | 0.010 |
| Open science | 0.002 | 0.006 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.006 | 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".