Bibliographic record
Abstract
We investigate how to efficiently compute the difference result of two (or multiple) conjunctive queries, which is the last operator in relational algebra to be unraveled. The standard approach in practical database systems is to materialize the results for every input query as a separate set, and then compute the difference of two (or multiple) sets. This approach is bottlenecked by the complexity of evaluating every input query individually, which could be very expensive, particularly when there are only a few results in the difference. In this paper, we introduce a new approach by exploiting the structural property of input queries and rewriting the original query by pushing the difference operator down as much as possible. We show that for a large class of difference queries, this approach can lead to a linear-time algorithm, in terms of the input size and (final) output size, i.e., the number of query results that survive from the difference operator. We complete this result by showing the hardness of computing the remaining difference queries in linear time. Although a linear-time algorithm is hard to achieve in general, we also provide some heuristics that can provably improve the standard approach. At last, we compare our approach with standard SQL engines over graph and benchmark datasets. The experiment results demonstrate order-of-magnitude speedups achieved by our approach over the vanilla SQL engine.
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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 | 0.019 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.013 |
| Open science | 0.005 | 0.004 |
| Research integrity | 0.001 | 0.003 |
| 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".