最小翻转超树问题的数据约简
Towards a Data Reduction for the Minimum Flip Supertree Problem
摘要：
在计算遗传学中，构造给定的有根输入树的超树的问题可以以不同的方式形式化，以处理输入中的矛盾信息。我们考虑最小翻转超树问题，其中输入树被转换成0/1/？矩阵，这样每一行代表一个分类单元，每一列代表一个输入树的内部节点。我们的目标是找到一个完美的同源性的输入矩阵，需要最少的0/1-翻转，即在矩阵中的0/1-项目的更正。这个问题是NP完全问题。在这里，我们提出了一个参数化的数据减少多项式运行时间。当且仅当原始实例有解时，数据约简保证约简实例有解。然后，我们通过使用上界使我们的数据简化参数无关。这允许我们对实例进行预处理，并使用任意方法求解简化的实例。不同于现有的共识树问题的数据约简，我们的约简允许我们对矩阵中的某些条目得出结论。我们已经实施并评估了我们的数据缩减。不幸的是，我们发现最小翻转超树问题在实践中也很难：随着实例变得越来越“复杂”，在数据缩减过程中可以导出的信息量会减少，并且“复杂”实例的运行时间很快变得令人望而却步。尽管如此，我们的方法为这个相关的系统发育问题提供了另一种攻击途径。
英文摘要：
In computational phylogenetics, the problem of constructing a supertree of a given set of rooted input trees can be formalized in different ways, to cope with contradictory information in the input. We consider the Minimum Flip Supertree problem, where the input trees are transformed into a 0/1/?-matrix, such that each row represents a taxon, and each column represents an inner node of one of the input trees. Our goal is to find a perfect phylogeny for the input matrix requiring a minimum number of 0/1-flips, that is, corrections of 0/1-entries in the matrix. The problem is known to be NP-complete. Here, we present a parameterized data reduction with polynomial running time. The data reduction guarantees that the reduced instance has a solution if and only if the original instance has a solution. We then make our data reduction parameter-independent by using upper bounds. This allows us to preprocess an instance, and to solve the reduced instance with an arbitrary method. Different from an existing data reduction for the consensus tree problem, our reduction allows us to draw conclusions about certain entries in the matrix. We have implemented and evaluated our data reduction. Unfortunately, we find that the Minimum Flip Supertree problem is also hard in practice: The amount of information that can be derived during data reduction diminishes as instances get more "complicated", and running times for "complicated" instances quickly become prohibitive. Still, our method offers another route of attack for this relevant phylogenetic problem.
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