A new method for generating compressed representation of transitive closure
Bibliographic record
Abstract
Let G(V, E) be a digraph (directed graph) with n nodes and e edges. Digraph G* = (V, E*) is the reflexive, transitive closure of G if (v, u) ∈ E* iff there is a path from v to u in G. If we store it as a matrix, O(n2) space is required, not suitable for large graphs. In this paper, we present a new method to reduce the space overhead to O(bn), where b is the G's width, defined to be the size of a largest node subset U of G such that for every pair of nodes u, v ∈ U, there does not exist a path from u to v or from v to u. With such a compressed data structure of transitive closure, the time for checking reachability (whether a node is reachable from another node through a path) is bounded by O(logb). In addition, this data structure can be generated in O(be') time, where e' is the size of a subset of E, which contains only those edges (u, v) such that there is no path of length ≥2 connecting u and v. We are able to show that the average value of e' is on the order of O(n1.5). Our method is suitable for both acyclic and cyclic graphs.
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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 | 0.000 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".