On the Parameterized Complexity of Pooling Design
Bibliographic record
Abstract
Pooling design is a very helpful tool for reducing the number of tests in DNA library screening, which is a key process to obtain high-quality DNA libraries for studying gene functions. Three basic problems in pooling design are, given an m x n binary matrix and a positive integer d, to decide whether the matrix is d-separable (d-separable, or d-disjunct). The three problems are all known to be coNP-complete. Since in most applications, d is a small integer compared to n, it is interesting to investigate whether there are efficient algorithms solving the above problems when the value of d is small. In this article, we give a negative answer to the above question by studying the parameterized complexity of these three problems, with d as the parameter. We show that the parameterized versions of all the three problems are co-W[2]-complete. An immediate implication of our results is that, given an m x n binary matrix and a positive integer d, a deterministic algorithm with running time f(d) x (mn)(O(1)) (where f is an arbitrary computable function) to decide whether the matrix is d-separable (d-separable, or d-disjunct) should not be expected.
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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 | 0.006 | 0.039 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.004 | 0.010 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.009 | 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".