Engineering Wavelet Tree Implementations for Compressed Web Graph Representations
Bibliographic record
Abstract
Summary form only given: We study compressed representations of web graphs. Among previous work, the solution by Hernandez and Navarro [1] supports more queries than alternative approaches, including in-neighbour queries, out-neighbour queries and a set of mining queries. Their main strategy is to extract dense subgraphs from the given graph, and encode them using succinct data structures such as wavelet trees. Previous experimental studies on wavelet trees, however, test performance using textual data, and more engineering work is needed for the data generated from web graphs.Our strategy is to use different implementations to encode bit vectors at different levels of the wavelet trees constructed for dense subgraphs, based on the observation that bit vectors at top levels are more compressible than the rest. These implementations are considered: RRR, practical implementations [2] of the structure by Raman et al. [3]; RLEG, a bit vector structure based on run-length and Elias gamma codes [4]; and Plain, an uncompressed representation with low overheads [5]. Two specific approaches are used to combine them: The first approach encodes bit vectors using RRR starting from the root of a wavelet tree, until a level for which Plain uses less space is reached. Then, starting from this level downwards, Plain is used to encode bit vectors. The second approach uses RLEG, RRR and Plain in a similar top-down fashion, and different tradeoffs can be achieved by using different block sizes for RLEG.We implemented these approaches with code from [1, 4] and the compact structures library libcds (http://recoded.cl/), to encode data sets from the WebGraph Framework project (http://webgraph.di.unimi.it/). We obtained a rich set of time/space tradeoffs that can not be achieved using a single bit vector structure for all levels. The following three tradeoffs are particularly interesting: A new encoding scheme that decreases the space cost of Hernandez and Navarro's structure by 9% to 19% (more than 13% for all but one graph), while only doubling query time; a new scheme that decreases the space cost by 4% to 12% (10% or more for most graphs), with roughly the same query time; and a new scheme that decreases the space cost and the query time by about 2% and 1%-9% (5% or more for most graphs), respectively.
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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 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".