Summary: A tanglegram is a pair of trees whose leaf sets are in one-to-one correspondence; matching leaves are connected by inter-tree edges. In applications such as phylogenetics or hierarchical clustering, 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 even for complete binary trees, for general binary trees the problem is hard to approximate if the unique games conjecture holds. In this paper, we present an extensive experimental comparison of a new and several known heuristics for the general binary case. We measure the performance of the heuristics with a simple integer linear program and a new exact branch-and-bound algorithm. The new heuristic returns the first solution that the branch-and-bound algorithm computes (in quadratic time). Surprisingly, in most cases this simple heuristic is at least as good as the best of the other heuristics.
For the entire collection see [Zbl 1280.68022].