The inversion distance, that is the distance between two unichromosomal genomes with the same content allowing only inversions of DNA segments, can be exactly computed thanks to a pioneering approach of Hannenhalli and Pevzner from 1995. In 2000, El-Mabrouk extended the inversion model to perform the comparison of unichromosomal genomes with unequal contents, combining inversions with insertions and deletions (indels) of DNA segments, giving rise to the inversion-indel distance. However, only a heuristic was provided for its computation. In 2005, Yancopoulos, Attie and Friedberg started a new branch of research by introducing the generic double cut and join (DCJ) operation, that can represent several genome rearrangements (including inversions). In 2006, Bergeron, Mixtacki and Stoye showed that the DCJ distance can be computed in linear time with a very simple procedure. As a consequence, in 2010 we gave a linear-time algorithm to compute the DCJ-indel distance. This result allowed the inversion-indel model to be revisited from another angle. In 2013, we could show that, when the diagram that represents the relation between the two compared genomes has no bad components , the inversion-indel distance is equal to the DCJ-indel distance. In the present work we complete the study of the inversion-indel distance by giving the first algorithm to compute it exactly even in the presence of bad components.

中文翻译：

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计算反演-Indel 距离

由于 Hannenhalli 和 Pevzner 从 1995 年开始的开创性方法，可以精确计算倒置距离，即具有相同内容的两个单染色体基因组之间的距离，仅允许 DNA 片段倒置。2000 年，El-Mabrouk 将倒置模型扩展到执行具有不相等内容的单染色体基因组的比较，将倒位与 DNA 片段的插入和缺失（indels）结合起来，从而产生倒位-indel 距离。然而，只为它的计算提供了一个启发式方法。2005 年，Yancopoulos、Attie 和 Friedberg 开始了一个新的研究分支，他们引入了通用的双切和连接 (DCJ) 操作，它可以代表几种基因组重排（包括倒位）。2006 年，伯杰龙，Mixtacki 和 Stoye 表明 DCJ 距离可以通过非常简单的程序在线性时间内计算。因此，在 2010 年，我们给出了一种线性时间算法来计算 DCJ-indel 距离。这一结果允许从另一个角度重新审视 inversion-indel 模型。在 2013 年，我们可以证明，当表示两个比较基因组之间关系的图表没有坏组件，inversion-indel 距离等于 DCJ-indel 距离。在目前的工作中，我们通过给出第一个算法来完成对 inversion-indel 距离的研究，即使在存在不良组件的情况下也能精确计算它。