Fast Exact MultiConstraint Shortest Path Algorithms
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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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".