Generalized Binary Tanglegrams: Algorithms and Applications

Several applications require the joint display of two phylogenetic trees whose leaves are matched by inter-tree edges. This issue arises, for example, when comparing gene trees and species trees or when studying the co-speciation of hosts and parasites. The tanglegram layout problem seeks to produce a layout of the two trees that minimizes the number of crossings between the inter-tree edges. This problem is well-studied for the case when the mappings between the leaves of the two trees is one-to-one. However, in typical biological applications, this mapping is seldom one-to-one. In this work we (i) define a generalization of the tanglegram layout problem, called the Generalized Tanglegram Layout (GTL) problem, which allows for arbitrary interconnections between the leaves of the two trees, (ii) provide efficient algorithms for the case when the layout of one tree is fixed, (iii) discuss the fixed parameter tractability and approximability of the GTL problem, (iv) formulate heuristic solutions for the GTL problem, and (v) evaluate our algorithms experimentally.