Sorting under partial (interval order) information
Bibliographic record
Abstract
In this paper we study how to efficiently order a set of imprecise points. In one dimension, the order of a set of points is their sorted order from low to high. A set of imprecise points in the preprocessing model consists of a set of $n$ uncertainty regions $\mathcal{R} = \{R_1, R_2, \ldots R_n \}$ and a set of $n$ points $P = \{ p_1, p_2, \ldots p_n\}$ such that for every $R_i \in \mathcal{R}$ there is an associated point $p_i \in P$ with $p_i \in P$. In one dimension, the set $\mathcal{R}$ is a set of intervals which induces a partial order such that the total order of the underlying true points $P$ extends that partial order. We show how to preprocess the partial order induced by $\mathcal{R}$, such that given the point set $P$ we can uncover the underlying total order in uncertainty-region optimal time. Specifically, we parametrize the degree of overlap by the intervals with a measure we call the ambiguity of the set $\mathcal{R}$ and we show that the ambiguity of $\mathcal{R}$ is a lower bound for the time required to sort the points $P$. This paper can be seen as a geometric variant of sorting under partial information, which is a well-studied topic within computer science.
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.
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.002 |
| Open science | 0.001 | 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".