Untangling Tanglegrams: Comparing Trees by Their Drawings

Tanglegrams Are Misleading for Visual Evaluation of Tree Congruence

“…The idea behind this visualization is straightforward: after having found the graphical layout that produces the minimum crossings of the lines linking both trees, the obtained tanglegram is expected to help in more clearly visualizing co-evolutionary relationships between species (Matsen et al 2016). Numerous studies focused on finding the best algorithm for reordering the leaves in order to produce the less entangled representation (Bansal et al 2009;Böcker et al 2009;Fernau, Kaufmann, Poths 2010;Venkatachalam et al 2010 and references therein; Scornavacca, Zickmann, Huson 2011). But none ever questioned the real utility of such representation for getting insight into the level of topological similarity (or congruence) between the compared trees.…”

A tanglegram Kuratowski theorem

“…Note that the (graph) crossing number of a tanglegram T is less or equal to the (tanglegram) crossing number of T , since the tanglegram layout is more restrictive than the graph drawing. The following proposition that provides an almost obvious characterization of planarity of tanglegram, was found by and later rediscovered : Proposition Assume that a tanglegram T is represented by the layout , and let the roots of L and R be r and ρ. Let denote the graph in which the underlying graph of T (consisting of the two binary trees and the matching edges) is augmented by the edge .…”

Tanglegrams for rooted phylogenetic trees and networks

“…For example, a number of articles (Bansal et al , 2009; Böcker et al , 2009; Buchin et al , 2009; Fernau et al , 2005; Nöllenburg et al , 2009; Venkatachalam et al , 2010). consider the One-Tree Crossing Minimization (OTCM) and the Two-Tree Crossing Minimization (TTCM) problems that both aim at minimizing the number of crossings between connectors.…”

“…In the former problem, the layout of one of the trees is fixed and that of the other is mutable whereas in the latter formulation the layout of both trees are allowed to be changed. For binary trees, OTCM is solvable in O ( n log n ) time (Venkatachalam et al , 2010), while TTCM is NP-complete (Fernau et al , 2010). In Dwyer and Schreiber (2004), the authors describe a ‘seesaw’ heuristic for the TTCM problem for binary (or bifurcating) trees, which operates by repeatedly solving the OTCM problem, each time switching the roles of the two trees.…”

“…Other approaches use fixed-parameter tractability (FPT) parameterized by the number k of connector crossings (Fernau et al , 2005). A generalization to non-binary trees is discussed in Venkatachalam et al (2010). The only algorithm that is able to compute tanglegrams for binary trees with many-to-many connections is described in Bansal et al (2009).…”