Decomposing DAGs into spanning trees: A new way to compress transitive closures
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 if (v, u) ∈ E* iff there is a path from v to u in G. Efficient storage of G* is important for supporting reachability queries which are not only common on graph databases, but also serve as fundamental operations used in many graph algorithms. A lot of strategies have been suggested based on the graph labeling, by which each node is assigned with certain labels such that the reachability of any two nodes through a path can be determined by their labels. Among them are interval labelling, chain decomposition, and 2-hop labeling. However, due to the very large size of many real world graphs, the computational cost and size of labels using existing methods would prove too expensive to be practical. In this paper, we propose a new approach to decompose a graph into a series of spanning trees which may share common edges, to transform a reachability query over a graph into a set of queries over trees. We demonstrate both analytically and empirically the efficiency and effectiveness of our method.
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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 | 0.001 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.006 | 0.008 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.007 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".