An asymptotic approximation algorithm for 3D-strip packing
Bibliographic record
Abstract
We present an asymptotic (2 + e)-approximation algorithm for the 3D-strip packing problem, for any e > 0. In the 3D-strip packing problem the input is a set L = {b1, b2,. . ., bn} of 3-dimensional boxes. Each box bi has width, length, and height at most 1. The problem is to pack the boxes into a 3-dimensional bin B of width 1, length 1 and minimum height, so that the boxes do not overlap. We consider here only orthogonal packings without rotations; this means that the boxes are packed so that their faces are parallel to the faces of the bin, and rotations are not allowed. This algorithm improves on the previously best algorithm of Miyazawa and Wakabayashi which has asymptotic performance ratio of 2.64. Our algorithm can be easily modified to a (4 + e)-approximation algorithm for the 3D-bin packing problem.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 0.005 |
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".