Haplotype Inferring via Galled-Tree Networks Is NP-Complete
Bibliographic record
Abstract
The problem of determining haplotypes from genotypes has gained considerable prominence in the research community since the beginning of the HapMap project. Here the focus is on determining the sets of SNP values of individual chromosomes (haplotypes), since such information better captures the genetic causes of diseases. One of the main algorithmic tools for haplotyping is based on the assumption that the evolutionary history for the original haplotypes satisfies perfect phylogeny. This tool can be applied only on individual blocks of chromosomes, in which it is assumed that recombinations do not happen. However, exact determination of blocks is usually not possible. It would be desirable to develop a method for haplotyping which can account for recombinations, and thus can be applied on multiblock sections of chromosomes. A natural candidate for such a method is haplotyping via phylogenetic networks (which model recombinations) or their simplified version: galled-tree networks. However, even haplotyping via galled-tree networks appears hard, as the efficient algorithms exist only for very special cases: the galled-tree network has either a single gall or only small galls with two mutations each. Building on our previous results, we show that, in general, haplotyping via galled-tree networks is NP-complete, and it remains NP-complete when galls are allowed to have at most k mutations, for any k ≥ 3.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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 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".