A binary tanglegram is a pair 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, 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 drawing 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 general binary trees. We show that the problem is hard even if both trees are complete binary trees. For this case we give an O(n 3)-time 2-approximation and a new and simple fixed-parameter algorithm. We show that the maximization version of the dual problem for general binary trees can be reduced to a version of MaxCut for which the algorithm of Goemans and Williamson yields a 0.878-approximation.
|Titel||Graph Drawing (16th International Symposium, GD'08, Heraklion, Crete, Greece, September 21-24, 2008, Revised Papers)|
|Redacteuren||I.G. Tollis, M. Patrignani|
|Plaats van productie||Berlin|
|ISBN van geprinte versie||978-3-642-00218-2|
|Status||Gepubliceerd - 2009|
|Naam||Lecture Notes in Computer Science|
|ISSN van geprinte versie||0302-9743|