The canadian traveller problem and its competitive analysis
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
From the online point of view, we study the Canadian Traveller Problem (CTP), in which the traveller knows in advance the structure of the graph and the costs of all edges. However, some edges may fail and the traveller only observes that upon reaching an adjacent vertex of the blocked edge. The goal is to find the least-cost route from the source O to the destination D, more precisely, to find an adaptive strategy minimizing the competitive ratio, which compares the performance of this strategy with that of a hypothetical offline algorithm that knows the entire topology in advance. In this paper, we present two adaptive strategies—a greedy or myopic strategy and a comparison strategy combining the greedy strategy and the reposition strategy in which the traveller backtracks to the source every time when he/she sees a failed edge. We prove tight competitive ratios of 2 k+1−1 and 2k+1 respectively for the two strategies, where k is the number of failed edges in the graph. Finally, we propose an explanation of why the greedy strategy and the comparison strategy are usually preferred by drivers in an urban traffic environment, based on an argument related to the length of the second-shortest path in a grid graph.
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.
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 | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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