BACKGROUND The evolutionary distance between two genomes can be estimated by computing a minimum length sequence of operations, called genome rearrangements, that transform one genome into another. Usually, a genome is modeled as an ordered sequence of genes, and most of the studies in the genome rearrangement literature consist in shaping biological scenarios into mathematical models. For instance, allowing different genome rearrangements operations at the same time, adding constraints to these rearrangements (e.g., each rearrangement can affect at most a given number of genes), considering that a rearrangement implies a cost depending on its length rather than a unit cost, etc. Most of the works, however, have overlooked some important features inside genomes, such as the presence of sequences of nucleotides between genes, called intergenic regions. RESULTS AND CONCLUSIONS In this work, we investigate the problem of computing the distance between two genomes, taking into account both gene order and intergenic sizes. The genome rearrangement operations we consider here are constrained types of reversals and transpositions, called super short reversals (SSRs) and super short transpositions (SSTs), which affect up to two (consecutive) genes. We denote by super short operations (SSOs) any SSR or SST. We show 3-approximation algorithms when the orientation of the genes is not considered when we allow SSRs, SSTs, or SSOs, and 5-approximation algorithms when considering the orientation for either SSRs or SSOs. We also show that these algorithms improve their approximation factors when the input permutation has a higher number of inversions, where the approximation factor decreases from 3 to either 2 or 1.5, and from 5 to either 3 or 2.

中文翻译：

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基因顺序和基因间大小的超短操作。

背景技术两个基因组之间的进化距离可以通过计算最小长度的操作序列来估计，称为基因组重排，它将一个基因组转换成另一个基因组。通常，基因组被建模为有序的基因序列，并且基因组重排文献中的大多数研究都在于将生物学场景塑造成数学模型。例如，允许同时进行不同的基因组重排操作，对这些重排添加限制（例如，每个重排最多可以影响给定数量的基因），考虑到重排意味着成本取决于其长度而不是单位成本然而，大多数工作都忽略了基因组内部的一些重要特征，例如基因之间核苷酸序列的存在，称为基因间区域。结果和结论 在这项工作中，我们研究了计算两个基因组之间距离的问题，同时考虑了基因顺序和基因间大小。我们在这里考虑的基因组重排操作是受限类型的反转和转座，称为超短反转 (SSR) 和超短转座 (SST)，它们最多影响两个（连续）基因。我们用超短操作 (SSO) 表示任何 SSR 或 SST。当我们允许 SSR、SST 或 SSO 时，当不考虑基因的方向时，我们展示 3 近似算法，而在考虑 SSR 或 SSO 的方向时，我们展示 5 近似算法。我们还表明，当输入排列具有更高数量的反转时，这些算法会提高它们的近似因子，