Conjunctive Queries on Probabilistic Graphs: The Limits of Approximability
Bibliographic record
Abstract
Query evaluation over probabilistic databases is a notoriously intractable problem - not only in combined complexity, but for many natural queries in data complexity as well [Antoine Amarilli et al., 2017; Nilesh N. Dalvi and Dan Suciu, 2012]. This motivates the study of probabilistic query evaluation through the lens of approximation algorithms, and particularly of combined FPRASes, whose runtime is polynomial in both the query and instance size. In this paper, we focus on tuple-independent probabilistic databases over binary signatures, which can be equivalently viewed as probabilistic graphs. We study in which cases we can devise combined FPRASes for probabilistic query evaluation in this setting. We settle the complexity of this problem for a variety of query and instance classes, by proving both approximability and (conditional) inapproximability results. This allows us to deduce many corollaries of possible independent interest. For example, we show how the results of [Marcelo Arenas et al., 2021] on counting fixed-length strings accepted by an NFA imply the existence of an FPRAS for the two-terminal network reliability problem on directed acyclic graphs: this was an open problem until now [Rico Zenklusen and Marco Laumanns, 2011]. We also show that one cannot extend a recent result [Timothy van Bremen and Kuldeep S. Meel, 2023] that gives a combined FPRAS for self-join-free conjunctive queries of bounded hypertree width on probabilistic databases: neither the bounded-hypertree-width condition nor the self-join-freeness hypothesis can be relaxed. Finally, we complement all our inapproximability results with unconditional lower bounds, showing that DNNF provenance circuits must have at least moderately exponential size in combined complexity.
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How this classification was reachedexpand
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 | 0.001 | 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 | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".