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Drawing (Complete) Binary Tanglegrams

Please always quote using this URN: urn:nbn:de:bvb:20-opus-124622
  • 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 GamesA 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.show moreshow less

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Metadaten
Author: Kevin Buchin, Maike Buchin, Jaroslaw Byrka, Martin Nöllenburg, Yoshio Okamoto, Rodrigo I. Silveira, Alexander Wolff
URN:urn:nbn:de:bvb:20-opus-124622
Document Type:Journal article
Faculties:Fakultät für Mathematik und Informatik / Institut für Informatik
Language:English
Parent Title (English):Algorithmica
Year of Completion:2012
Volume:62
Pagenumber:309-332
Source:Algorithmica (2012) 62:309–332. doi:10.1007/s00453-010-9456-3
DOI:https://doi.org/10.1007/s00453-010-9456-3
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
Tag:NP-hardness; approximation algorithm; binary tanglegram; crossing minimization; fixed-parameter tractability
Release Date:2016/01/20
Licence (German):License LogoCC BY-NC: Creative-Commons-Lizenz: Namensnennung, Nicht kommerziell