Query result size estimation using a novel histogram-like technique: the rectangular attribute cardinality map
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Current database systems utilize histograms to approximate frequency distributions of attribute values of relations. These are used to efficiently estimate query result sizes and access plan costs. Even though they have been in use for nearly two decades, there has been no significant mathematical techniques (other than those used in statistics for traditional histogram approximations) to study them. We introduce a new histogram-like approximation strategy called the Rectangular Attribute Cardinality Map (R-ACM), that aims to approximate the density of the underlying attribute values using the philosophies of numerical integration. In this new histogram-like approximation method, the density function within a given sector is approximated by a rectangular cell, where the height of the cell is obtained so as to guarantee that the actual probability density differs from the approximated one by a maximum of a user specified tolerance, /spl tau/. Furthermore, unlike the two traditional histogram types, namely equi-width and equi-depth, the R-ACM is neither equi-width nor equi-depth. Analytically, we show that for the R-ACM, the distribution of an attribute value within the sector is binomially distributed. This permits us to derive worst-case and average case results for the estimation errors of the probability mass itself. Our theoretical results, which include a rigorous maximum likelihood and expected case analyses, and an extensive set of experiments demonstrate that the R-ACM scheme (which is essentially histogram-like) is much more accurate than the traditional histograms for query result size estimation. Due to its high accuracy and low construction costs, we hope that it could become an invaluable tool for query optimization in the future database systems.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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