Semi-dynamic algorithms for strongly chordal graphs
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Bibliographic record
Abstract
Within the broad ambit of algorithm design, the study of dynamic graph algorithms continues to be a thriving area of research. Commensurate with this interest is an extensive literature on the topic. Not surprisingly, dynamic algorithms for all varieties of shortest path problems, in view of their practical importance, occupy a preeminent position. Relevant to this paper are fully dynamic algorithms for chordal graphs. Surprisingly, to the best of our knowledge, there seems to be no reported results for the problem of dynamic algorithms for strongly chordal graphs. To redress this gap, in this paper, we propose a semi-dynamic algorithm for edge-deletions and a semi-dynamic algorithm for edge-insertions in a strongly chordal graph, [Formula: see text]. The query complexity of an edge-deletion is [Formula: see text], where [Formula: see text] and [Formula: see text] are the degrees of the vertices [Formula: see text] and [Formula: see text] of the candidate edge [Formula: see text], while the query complexity of an edge-insertion is [Formula: see text], where [Formula: see text] is the number of vertices of [Formula: see text].
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| 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