Fast Exact MultiConstraint Shortest Path Algorithms
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Bibliographic record
Abstract
QoS routing has been shown to be NP-hard. A recent study of its hardness shows that the "worst-case" may not occur in practice (Kuipers mieghem, 2003). This suggests that there may exist fast exact algorithms for the multi-constraint shortest path (MCSP) problem, an instance of QoS routing. Search techniques such as A* and IDA* may solve hard problems exactly in polynomial time. In Li et al. (2005), we deploy the idea of iterative deepening search to design IDA*_MCSP, and show its efficiency by extensive empirical study. In this paper, we show that for infeasible cases, where there is no feasible solution, IDA*_MCSP may not be as efficient as A*Prune. This motivates us to design an algorithm that is efficient in both feasible and infeasible cases. We design an exact MCSP algorithm A*_MCSP, which introduces the state notion and dominance relationship between states. Furthermore, we design an exact MCSP algorithm FringeMCSP. It can be regarded as an integration of IDA*_MCSP and A*_MCSP. Extensive empirical study shows that FringeMCSP has good performance in both feasible and infeasible cases; while IDA*_MCSP still shows its superiority among the proposed MCSP algorithms in feasible cases.
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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 | 0.000 | 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 | 0.000 |
| 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