Succinct and Compact Data Structures for Intersection Graphs
Bibliographic record
Abstract
This thesis designs space efficient data structures for several classes of intersection graphs, including interval graphs, path graphs and chordal graphs. Our goal is to support navigational operations such as adjacent and neighbourhood and distance operations such as distance efficiently while occupying optimal space, or a constant factor of the optimal space. \n \nUsing our techniques, we first resolve an open problem with regards to succinctly representing ordinal trees that is able to convert between the index of a node in a depth-first traversal (i.e. pre-order) and in a breadth-first traversal (i.e. level-order) of the tree. Using this, we are able to augment previous succinct data structures for interval graphs with the $\\GDistance$ operation. \n \nWe also study several variations of the data structure problem in interval graphs: beer interval graphs and dynamic interval graphs. In beer interval graphs, we are given that some vertices of the graph are beer nodes (representing beer stores) and we consider only those paths that pass through at least one of these beer nodes. We give data structure results and prove space lower bounds for these graphs. We study dynamic interval graphs under several well known dynamic models such as incremental or offline, and we give data structures for each of these models. \n \nFinally we consider path graphs where we improve on previous works by exploiting orthogonal range reporting data structures. For optimal space representations, we improve the run time of the queries, while for non-optimal space representations (but optimal query times), we reduce the space needed.
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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 | 0.004 | 0.021 |
| Meta-epidemiology (narrow) | 0.001 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.008 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.007 | 0.024 |
| Open science | 0.006 | 0.008 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.010 | 0.003 |
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".