General spanning trees and reachability query evaluation
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
Graph reachability is fundamental to a wide range of applications, including CAD/CAM, CASE, office systems, software management, as well as geographical navigation and internet routing. Many applications involve huge graphs and requires fast answering of reachability queries. Several reachability labeling methods have been proposed for this purpose. They assign labels to the nodes, such that the reachability between any two nodes can be determined using their labels only. In this paper, we propose a new data structure, called a general spanning tree of a directed acyclic graph (DAG) to minimize label space. Different from a traditional spanning tree, an edge in a general spanning tree T of a DAG G may corresponds to a path in G. That is, for each edge u → v in T, we have a path from u to v in G. An algorithm is discussed to find such a tree with the least number of leaf nodes in O(bn √b) time, where n is the number of the nodes of G, and b is the number of the leaf nodes of T. It can be proven that b equals 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. Based on T, we are able to reduce the label space to O(bn) with O(logb) reachability query time. Our method can also be extended for graphs containing cycles.
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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 | 0.001 | 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 | 0.001 |
| 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