Scaling Up Search with Partial Initial States in Optimization Crosswords
Bibliographic record
Abstract
Heuristic search remains a leading approach to difficult combinatorial optimization problems. Search algorithms can utilize pruning based on comparing a target score with an admissible (optimistic) estimate of the best score that can be achieved from a given state. If the former is larger they prune the state. However, when the target score is too high the search can fail by exhausting the space without finding a solution. In this paper we show that such failed searches can still be valuable. Specifically, best partial solutions encountered in such failed searches can often bear a high similarity to the corresponding part of a full high-quality or even optimal solution. Thus, a new search for a full solution, with a lower target score, can start with a best known partial solution, rather than starting from scratch. We demonstrate our ideas in a constraint optimization problem modelled on the Romanian Crosswords Competition, a challenging problem where humans perform much better than computers. Utilizing partial solutions produced by a failed search cuts down the running time of an existing state-of-the-art solver by orders of magnitude on competition-level crossword puzzle instances and allows to solve more instances.
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 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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".