Succinct Data Structures for Path Graphs and Chordal Graphs Revisited
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
We enhance space efficient representations of two types of intersection graphs. We refine the data structure for path graphs of Balakrishnan et al. to give a succinct data structure of n log n + o(n log n) bits that supports adjacency test, degree and neighbourhood queries in $O\left( {\frac{{\log n}}{{\log \log n}}} \right)$ time (for neighbourhood queries, this is the amount of time for each neighbour reported). To achieve O(1) query times, we give a data structure using (3 + ε)n log n + o(n log n) bits for any constant ε > 0. Furthermore, we are able to support both the distance and shortest path queries on unweighted path graphs using (2 + ε)n log n+ o(n log n) bits in O(log n/ log log n) time (shortest path uses an additional O(1) time per vertex on the path). This is the first compact distance oracles for path graphs. Turning to chordal graphs, we enhance the succinct data structure of Munro and Wu to reduce all query times including performing adjacency test in O(1) time.
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.
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 | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| 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