12462
2012
eng
309-332
62
article
1
2016-01-19
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Drawing (Complete) Binary Tanglegrams
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.
Algorithmica
10.1007/s00453-010-9456-3
urn:nbn:de:bvb:20-opus-124622
Algorithmica (2012) 62:309–332. doi:10.1007/s00453-010-9456-3
Kevin Buchin
Maike Buchin
Jaroslaw Byrka
Martin Nöllenburg
Yoshio Okamoto
Rodrigo I. Silveira
Alexander Wolff
eng
uncontrolled
NP-hardness
eng
uncontrolled
crossing minimization
eng
uncontrolled
binary tanglegram
eng
uncontrolled
approximation algorithm
eng
uncontrolled
fixed-parameter tractability
Datenverarbeitung; Informatik
open_access
Institut für Informatik
Universität Würzburg
https://opus.bibliothek.uni-wuerzburg.de/files/12462/art_10.1007_s00453-010-9456-3.pdf