Comparing Genomes with Duplications: A Computational Complexity Point of View
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Bibliographic record
Abstract
In this paper, we are interested in the computational complexity of computing (dis)similarity measures between two genomes when they contain duplicated genes or genomic markers, a problem that happens frequently when comparing whole nuclear genomes. Recently, several methods ( [1], [2]) have been proposed that are based on two steps to compute a given (dis)similarity measure M between two genomes G_1 and G_2: first, one establishes a oneto- one correspondence between genes of G_1 and genes of G_2 ; second, once this correspondence is established, it defines explicitly a permutation and it is then possible to quantify their similarity using classical measures defined for permutations, like the number of breakpoints. Hence these methods rely on two elements: a way to establish a one-to-one correspondence between genes of a pair of genomes, and a (dis)similarity measure for permutations. The problem is then, given a (dis)similarity measure for permutations, to compute a correspondence that defines an optimal permutation for this measure. We are interested here in two models to compute a one-to-one correspondence: the exemplar model, where all but one copy are deleted in both genomes for each gene family, and the matching model, that computes a maximal correspondence for each gene family. We show that for these two models, and for three (dis)similarity measures on permutations, namely the number of common intervals, the maximum adjacency disruption (MAD) number and the summed adjacency disruption (SAD) number, the problem of computing an optimal correspondence is NP-complete, and even APXhard for the MAD number and SAD number.
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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 it