关于基因组比较的近似性
On the Approximability of Comparing Genomes with Duplicates
摘要：
比较基因组学中的一个中心问题在于计算两个基因组之间的（不）相似性度量，例如为了构建同源性。所有现有的措施都是在基因组上定义的，没有重复。然而，我们知道基因可以在同一个基因组中复制。克服这一困难的一种可能的方法是在两个基因组的基因之间建立一对一的对应关系（即匹配），其中选择对应关系以优化所研究的测量。在本文中，我们感兴趣的三个措施（断点的数量，数量的共同区间和数量的保守区间）和三个模型的匹配（范例，中间和最大匹配模型）。我们证明，对于每个模型和每个措施M，计算两个基因组之间的匹配，优化M是APX困难的。我们还研究了以下问题的复杂性：是否有一个范例（分别）。中间/最大匹配），不引起断点？我们证明了这个问题是NP完全的样本模型的一类新的实例，我们表明，这个问题是在P的最大匹配模型。我们还专注于第四个措施：邻接的数量，我们给出了几个近似算法的最大匹配模型，在基因组中包含相同数量的每个基因的重复的情况下。
英文摘要：
A central problem in comparative genomics consists in computing a (dis-)similarity measure between two genomes, e.g. in order to construct a phylogeny. All the existing measures are defined on genomes without duplicates. However, we know that genes can be duplicated within the same genome. One possible approach to overcome this difficulty is to establish a one-to-one correspondence (i.e. a matching) between genes of both genomes, where the correspondence is chosen in order to optimize the studied measure. In this paper, we are interested in three measures (number of breakpoints, number of common intervals and number of conserved intervals) and three models of matching (exemplar, intermediate and maximum matching models). We prove that, for each model and each measure M, computing a matching between two genomes that optimizes M is APX-hard. We also study the complexity of the following problem: is there an exemplarization (resp. an intermediate/maximum matching) that induces no breakpoint? We prove the problem to be NP-Complete in the exemplar model for a new class of instances, and we show that the problem is in P in the maximum matching model. We also focus on a fourth measure: the number of adjacencies, for which we give several approximation algorithms in the maximum matching model, in the case where genomes contain the same number of duplications of each gene.
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