Bibliographic record
Abstract
This thesis presents a number of results related to path traversal in trees and graphs. In particular, we focus on data structures which allow such traversals to be performed efficiently in the external memory setting. In addition, for trees and planar graphs the data structures we present are succinct. Our tree structures permit efficient bottom-up path traversal in rooted trees of arbitrary degree and efficient top-down path traversal in binary trees. In the graph setting, we permit efficient traversal of an arbitrary path in bounded degree planar graphs. Our data structures for both trees and graphs match or slightly improve current best results for external memory path traversal in these settings while at the same time improving space bounds due to the succinct nature of our data structures. Employing our path traversal structure for bounded degree planar graphs, we describe a number of useful applications of this technique for triangular meshes in R^2. As an extension of the R^2 representation for triangular meshes we also present an efficient external memory representation for well-shaped tetrahedral meshes in R^3. The external memory representation we present is based on a partitioning scheme that matches the current best-known results for well-shaped tetrahedral meshes. We describe applications of path traversal in tetrahedral meshes which are made efficient in the external memory setting using our structure. Finally, we present a result on using jump-and-walk point location in well-shaped meshes in both R^2 and R^3. We demonstrate that, given an approximate nearest neighbour from among the vertices of a mesh, locating the simplex containing the query point involves a constant length walk (path traversal) in the mesh.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.004 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.004 | 0.009 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.015 | 0.005 |
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".