Bibliographic record
Abstract
The task of determining which LEGO bricks to use to construct a volume is known as the LEGO Construction Problem. This is a challenging problem because even small volumes can be constructed in a tremendously large number of ways. As a result, an exhaustive search is impractical, and more nuanced search strategies must be employed to find a good, though not necessarily optimal, solution. This paper describes a multi-phase search approach to the LEGO Construction Problem. Our first search phase uses heuristics to identify a moderate number of candidates for each layer in the model. This is followed by two different search strategies which identify alternative brick arrangements that reduce the number of connected components, undesirable edges, and bricks in the model. A final highly localized search is applied to bricks at the boundaries between the model's connected components if the previous search processes fail to reduce the model to a single connected component. Applying this four-phase search strategy to a diverse selection of models has demonstrated that it normally finds a result that consists of a single connected component when such a solution exists, and that the models are structurally sound when built.
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.
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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 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".