遗传树上的最大简约距离：一个线性核常因子近似算法
Maximum parsimony distance on phylogenetictrees: a linear kernel and constant factor approximation algorithm
摘要：
最大简约距离是用来量化两个无根系统发生树的相异性的度量。它是NP难计算的，并且由于其复杂的组合结构，很少有积极的算法结果。在这里，我们解决这个缺点，表明问题是固定参数易处理的。我们通过建立一个线性核来做到这一点，即，在应用某些归约规则之后，所得到的实例具有由距离的线性函数限定的大小。作为这一结果的有力推论，我们证明了这个问题允许多项式时间常数因子近似算法;在遗传学中遇到的自然辅助图结构的树宽是有界的距离的函数;并且距离是在两棵树的最大协议森林的大小的常数因子内，这是遗传学中的一个很好的研究对象。
英文摘要：
Maximum parsimony distance is a measure used to quantify the dissimilarity of two unrooted phylogenetic trees. It is NP-hard to compute, and very few positive algorithmic results are known due to its complex combinatorial structure. Here we address this shortcoming by showing that the problem is fixed parameter tractable. We do this by establishing a linear kernel i.e., that after applying certain reduction rules the resulting instance has size that is bounded by a linear function of the distance. As powerful corollaries to this result we prove that the problem permits a polynomial-time constant-factor approximation algorithm; that the treewidth of a natural auxiliary graph structure encountered in phylogenetics is bounded by a function of the distance; and that the distance is within a constant factor of the size of a maximum agreement forest of the two trees, a well studied object in phylogenetics.
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