@article{BuchinBuchinByrkaetal.2012, author = {Buchin, Kevin and Buchin, Maike and Byrka, Jaroslaw and N{\"o}llenburg, Martin and Okamoto, Yoshio and Silveira, Rodrigo I. and Wolff, Alexander}, title = {Drawing (Complete) Binary Tanglegrams}, series = {Algorithmica}, volume = {62}, journal = {Algorithmica}, doi = {10.1007/s00453-010-9456-3}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-124622}, pages = {309-332}, year = {2012}, abstract = {A binary tanglegram is a drawing of a pair of rooted 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, it is essential that both trees are drawn without edge crossings and that the inter-tree edges have as few crossings as possible. It is known that finding a tanglegram with the minimum number of crossings is NP-hard and that the problem is fixed-parameter tractable with respect to that number. We prove that under the Unique Games Conjecture there is no constant-factor approximation for binary trees. We show that the problem is NP-hard even if both trees are complete binary trees. For this case we give an O(n 3)-time 2-approximation and a new, simple fixed-parameter algorithm. We show that the maximization version of the dual problem for binary trees can be reduced to a version of MaxCut for which the algorithm of Goemans and Williamson yields a 0.878-approximation.}, language = {en} }