@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}
}