The power of knowledge in linear search for an escaping target
Bibliographic record
Abstract
We consider linear search for an escaping target whose speed and/or initial distance from the origin may be unknown to the searcher. The searcher (an autonomous mobile agent) is initially placed at the origin of the real line and can move with maximum speed 1 in either direction along the line. The oblivious mobile target that is moving away from the origin with a constant speed v < 1 is initially placed by an adversary on the infinite line at distance d from the origin in an unknown direction. We consider four cases, depending on whether v and/or d is known to the searcher. The main contributions of this paper are new lower bounds as well as algorithms leading to new upper bounds for search in these settings. We present tight bounds for the cases when v is known. For the cases where v is unknown, we prove an optimal (up to lower order terms in the exponent) competitive ratio in the case where d is known and improved upper and lower bounds for the case where d is unknown. These results solve an open problem proposed in Coleman et al. (2022) [11] .
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How this classification was reachedexpand
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 | 0.002 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".