Maximum parsimony distance on phylogenetic trees: A linear kernel and constant factor approximation algorithm

Maximum parsimony distance is a measure used to quantify the dissimilarity of two unrooted phylogenetic trees. It NP-hard compute, and very few positive algorithmic results are known due its complex combinatorial structure. Here we address this shortcoming by showing that problem fixed parameter tractable. We do establishing linear kernel i.e., after applying certain reduction rules resulting instance has size bounded function distance. As powerful corollaries result prove permits polynomial-time constant-factor approximation algorithm; treewidth natural auxiliary graph structure encountered in phylogenetics distance; within constant factor maximum agreement forest trees, well studied object phylogenetics.