一种确定加权基因组重排距离的路径变形框架
A path-deformation framework for determining weighted genome rearrangement distance
摘要：
在倒置过程中测量两个细菌基因组之间的距离通常是通过假设所有倒置以相等的概率发生来完成的。近年来，人们提出了一种利用群论计算反演距离的方法，该方法对只有很短反演时间的模型是有效的。在本文中，我们展示了如何使用群论框架来建立最小距离的任何加权集的反演，推广以前的方法。要做到这一点，我们使用的重写系统的理论组，并利用Knuth-Benziran算法，第一次将这一理论引入到基因组重排问题。该方法的中心思想是使用现有的群论方法在基因组空间中找到两个基因组之间的初始路径（例如仅使用短反转），然后使用由Knuth-Benzirn算法生成的重写规则的汇合系统将该路径变形为最优。
英文摘要：
Measuring the distance between two bacterial genomes under the inversion process is usually done by assuming all inversions to occur with equal probability. Recently, an approach to calculating inversion distance using group theory was introduced, and is effective for the model in which only very short inversions occur. In this paper, we show how to use the group-theoretic framework to establish minimal distance for any weighting on the set of inversions, generalizing previous approaches. To do this we use the theory of rewriting systems for groups, and exploit the Knuth--Bendix algorithm, the first time this theory has been introduced into genome rearrangement problems. The central idea of the approach is to use existing group theoretic methods to find an initial path between two genomes in genome space (for instance using only short inversions), and then to deform this path to optimality using a confluent system of rewriting rules generated by the Knuth--Bendix algorithm.
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