An Overview of Reachability Indexes on Graphs
Bibliographic record
Abstract
Graphs have been the natural choice for modeling entities and the relationships among them. One of the most fundamental graph processing operators is a reachability query, which checks whether a path exists from the source to the target vertex in a plain graph, and additionally whether the path can satisfy a given path constraint based on the edge labels in an edge-labeled graph. Processing reachability queries requires potentially visiting a large portion of the graph due to the inherent transitivity of these queries. This makes it costly to evaluate them on large graphs. Thus, significant effort has been spent to design indexing techniques for reachability queries in the last three decades, building advanced data structures to efficiently compress the transitive closure of the graph so as to accelerate online query processing, aka reachability indexes. In this tutorial, we provide an in-depth technical review of the existing reachability indexes, ranging from those designed for plain graphs to ones for edge-labeled graphs. We conclude the tutorial by summarizing the open challenges for integrating these techniques into GDBMSs.
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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 | 0.002 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.008 | 0.017 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.007 | 0.017 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.008 | 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".