Efficient algorithms for centers and medians in interval and circular‐arc graphs
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Bibliographic record
Abstract
Abstract The p ‐center problem is to locate p facilities on a network so as to minimize the largest distance from a demand point to its nearest facility. The p ‐median problem is to locate p facilities on a network so as to minimize the average distance from a demand point to its closest facility. We consider these problems when the network can be modeled by an interval or circular‐arc graph whose edges have unit lengths. We provide, given the interval model of an n vertex interval graph, an O ( n ) time algorithm for the 1‐median problem on the interval graph. We also show how to solve the p ‐median problem, for arbitrary p , on an interval graph in O ( pn log n ) time and on a circular‐arc graph in O ( pn 2 log n ) time. We introduce a spring representation of the objective function and show how to solve the p ‐center problem on a circular‐arc graph in O ( pn ) time, assuming that the arc endpoints are sorted. © 2002 Wiley Periodicals, Inc.
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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)
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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