an:06882155
Zbl 1395.05171
Kelk, Steven; Stamoulis, Georgios; Wu, Taoyang
Treewidth distance on phylogenetic trees
EN
Theor. Comput. Sci. 731, 99-117 (2018).
0304-3975
2018
j
05C85 05C05 92D15
graph theory; phylogenetics; treewidth; algorithmic graph theory; computational biology
Summary: In this article we study the treewidth of the \textit{display graph}, an auxiliary graph structure obtained from the fusion of phylogenetic (i.e., evolutionary) trees at their leaves. Earlier work has shown that the treewidth of the display graph is bounded if the trees are in some formal sense topologically similar. Here we further expand upon this relationship. We analyze a number of reduction rules, commonly used in the phylogenetics literature to obtain fixed parameter tractable algorithms. In some cases (the \textit{subtree} reduction) the reduction rules behave similarly with respect to treewidth, while others (the \textit{cluster} reduction) behave very differently, and the behavior of the \textit{chain reduction} is particularly intriguing because of its link with graph separators and forbidden minors. We also show that the gap between treewidth and Tree Bisection and Reconnect (TBR) distance can be infinitely large, and that unlike, for example, planar graphs the treewidth of the display graph can be as much as linear in its number of vertices. A number of other auxiliary results are given. We conclude with a discussion and list a number of open problems.