Approximating Queries on Probabilistic Graphs
Bibliographic record
Abstract
Query evaluation over probabilistic databases is notoriously intractable -- not only in combined complexity, but often in data complexity as well. This motivates the study of approximation algorithms, and particularly of combined FPRASes, with runtime polynomial in both the query and instance size. In this paper, we focus on tuple-independent probabilistic databases over binary signatures, i.e., probabilistic graphs, and study when we can devise combined FPRASes for probabilistic query evaluation. We settle the complexity of this problem for a variety of query and instance classes, by proving both approximability results and (conditional) inapproximability results together with (unconditional) DNNF provenance circuit size lower bounds. This allows us to deduce many corollaries of possible independent interest. For example, we show how the results of Arenas et al. [ACJR21a] 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, a question asked by Zenklusen and Laumanns [ZL11]. We also show that one cannot extend a recent result of van Bremen and Meel [vBM23] giving 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. We last show how our methods can give insights on the evaluation and approximability of regular path queries (RPQs) on probabilistic graphs in the data complexity perspective, showing in particular that some of them are (conditionally) inapproximable.
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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 | 0.005 | 0.042 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.012 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".