  Tanglegrams are drawings of two rooted binary phylogenetic trees and a
matching between their leaf sets. The trees are drawn crossing-free on opposite
sides with their leaf sets facing each other on two vertical lines. Instead of
minimizing the number of pairwise edge crossings, we consider the problem of
minimizing the number of block crossings, that is, two bundles of lines
crossing each other locally. With one tree fixed, the leaves of the second tree
can be permuted according to its tree structure. We give a complete picture of
the algorithmic complexity of minimizing block crossings in one-sided
tanglegrams by showing NP-completeness, constant-factor approximations, and a
fixed-parameter algorithm. We also state first results for non-binary trees.
