Approximate truthful mechanisms for the knapsack problem, and negative results using a stack model for local ratio algorithms
Bibliographic record
Abstract
This thesis examines two topics in approximation algorithms. Mechanism design considers algorithmic problems in which agents behave based on selfish needs, rather than the will of the mechanism. For the knapsack problem, a number of approximate mechanisms are described that guarantees truthful agent behavior, including an FPTAS recently constructed by Alberto Marchetti-Spaccamela. Results relating truthfulness to the priority algorithm framework of Borodin, Nielsen and Rackoff are shown. A formal algorithmic model, called the stack algorithm, is defined, that captures the behavior of the local ratio method. The bandwidth problem is defined, and limitations are shown on the approximation power of the stack algorithm in a number of variations, including 2 machine scheduling. For covering problems, approximation lower bounds are shown for the Steiner tree and set cover problems.
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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 | 0.012 | 0.045 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.002 | 0.007 |
| Scholarly communication | 0.006 | 0.019 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.003 | 0.008 |
| Insufficient payload (model declined to judge) | 0.005 | 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".