TY  - JOUR
A1  - Buchin, Kevin
A1  - Buchin, Maike
A1  - Byrka, Jaroslaw
A1  - Nöllenburg, Martin
A1  - Okamoto, Yoshio
A1  - Silveira, Rodrigo I.
A1  - Wolff, Alexander
T1  - Drawing (Complete) Binary Tanglegrams
JF  - Algorithmica
N2  - 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.
KW  - NP-hardness
KW  - crossing minimization
KW  - binary tanglegram
KW  - approximation algorithm
KW  - fixed-parameter tractability
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-124622
VL  - 62
ER  -