Drawing Binary Tanglegrams: An Experimental Evaluation

TL;DR

This paper evaluates various algorithms for drawing binary tanglegrams with minimal crossings, comparing their effectiveness through experimental analysis in applications like phylogenetics and software engineering.

Contribution

It provides an experimental comparison of existing algorithms and an optimal integer quadratic programming approach for the tanglegram layout problem.

Findings

The integer quadratic program finds optimal solutions.

Recursive and hierarchy algorithms are faster but less optimal.

The study offers insights into algorithm performance for crossing minimization.

Abstract

A binary tanglegram is a pair <S,T> of binary trees whose leaf sets are in one-to-one correspondence; matching leaves are connected by inter-tree edges. For applications, for example in phylogenetics or software engineering, it is required that the individual trees are drawn crossing-free. A natural optimization problem, denoted tanglegram layout problem, is thus to minimize the number of crossings between inter-tree edges. The tanglegram layout problem is NP-hard and is currently considered both in application domains and theory. In this paper we present an experimental comparison of a recursive algorithm of Buchin et al., our variant of their algorithm, the algorithm hierarchy sort of Holten and van Wijk, and an integer quadratic program that yields optimal solutions.