Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs
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Bibliographic record
Abstract
This paper presents the first fully dynamic algorithms for maintaining all-pairs shortest paths in digraphs with positive integer weights less than b. For approximate shortest paths with an error factor of (2+/spl epsiv/), for any positive constant /spl epsiv/, the amortized update time is O(n/sup 2/ log/sup 2/ n/log log n); for an error factor of (1+/spl epsiv/) the amortized update time is O(n/sup 2/ log/sup 3/ (bn)//spl epsiv//sup 2/). For exact shortest paths the amortized update time is O(n/sup 2.5/ /spl radic/(b log n)). Query time for exact and approximate shortest distances is O(1); exact time and approximate paths can be generated in time proportional to their lengths. Also presented is a fully dynamic transitive closure algorithm with update time O(n/sup 2/ log n) and query time O(1). The previously known fully dynamic transitive closure algorithm with fast query time has one-sided error and update time O(n/sup 2.28/). The algorithms use simple data structures, and are deterministic.
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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) | 0.000 | 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 | 0.000 |
| 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