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.

最大简约距离是用于量化两个无根系统发育树的不相似性的度量。它是NP难以计算的，由于其复杂的组合结构，很少有积极的算法结果可知。在这里，我们通过显示问题是固定参数可处理的来解决此缺点。我们通过建立线性核来做到这一点，即在应用某些简化规则后，所得实例的大小受距离的线性函数限制。作为对该结果的有力推论，我们证明了该问题允许多项式时间恒定因子近似算法；在系统发育学中遇到的自然辅助图结构的树宽受距离的函数限制；