I/O-efficient shortest path algorithms for undirected graphs with random or bounded edge lengths
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Bibliographic record
Abstract
We present I/O-efficient single-source shortest path algorithms for undirected graphs. Our main result is an algorithm with I/O complexity O(√( nm log L )/ B +MST( n, m )) on graphs with n vertices, m edges, and arbitrary edge lengths between 1 and L ; MST( n, m denotes the I/O complexity of computing a minimum spanning tree; B denotes the disk block size. If the edge lengths are drawn uniformly at random from (0,1], the expected I/O complexity of the algorithm is O(√ nm/B + ( m/B )log B + MST( n, m )). A simpler algorithm has expected I/O complexity O(√( nm log B )/ B + MST( n, m )) for uniformly random edge lengths.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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