Finding Smallest Witnesses for Conjunctive Queries
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
A witness is a sub-database that preserves the query results of the original database, but of a much smaller size. It has wide applications in query rewriting and debugging, query explanation, IoT analytics, multi-layer network routing, and so on. In this article, we study the smallest witness problem ( SWP ) for the class of conjunctive queries (CQs) without self-joins. We first establish the dichotomy that SWP for a CQ can be computed in polynomial time if and only if it has head-cluster property , unless P = NP . Furthermore, we discover the dichotomy that SWP for a CQ with head-cluster property can be computed in linear time if and only if it is acyclic, assuming some well-known conjectures. We next turn to the approximated version by relaxing the size of a witness from being minimum. We surprisingly find that the head-domination property—that has been identified for the deletion propagation problem [ 40 ]—can also precisely capture the hardness of the approximated smallest witness problem. In polynomial time, SWP for any CQ with head-domination property can be approximated within a constant factor, while SWP for any CQ without such a property cannot be approximated within a logarithmic factor, unless P = NP . We further explore efficient approximation algorithms for CQs without the head-domination property: (1) we show a trivial algorithm that achieves a polynomially large approximation ratio for general CQs; (2) for any CQ with only one non-output attribute, such as star CQs, we show a greedy algorithm with a logarithmic approximation ratio; (3) for line CQs, which contain at least two non-output attributes, we relate SWP problem to the directed Steiner forest problem, whose algorithms can be applied to line CQs directly. Meanwhile, we establish an exponentially larger lower bound than above. It remains open to close the gap between the lower and upper bounds of the approximated SWP for CQs without the head-domination property.
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 | 0.000 | 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 | 0.001 | 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