Structure Detection in Mixed-Integer Programs
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
Despite vast improvements in computational power, many large-scale optimization problems involving integer variables remain difficult to solve. Certain classes, however, can be efficiently solved by exploiting special structure. One such structure is the singly bordered block-diagonal (BBD) structure that lends itself to Dantzig-Wolfe decomposition, Lagrangian relaxation, and branch and price. We start by introducing a new measure of goodness to capture desired features in BBD structures such as granularity of the structure, homogeneity of the block sizes, and isomorphism of the blocks. We then use it to propose a new approach to identify the best BBD structure inherent in the constraint matrix. The main building block of the proposed approach is the use of a community detection methodology in lieu of graph/hypergraph partitioning methods to alleviate one major drawback of the existing approaches in the literature: predefining the number of blocks. When tested on MIPLIB2003/2010 instances and compared against the state-of-the-art technique, the proposed algorithm is found to identify very good structures and require shorter CPU time to reach comparable bounds, in most cases.
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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