## 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.…

Author: | Kevin Buchin, Maike Buchin, Jaroslaw Byrka, Martin Nöllenburg, Yoshio Okamoto, Rodrigo I. Silveira, Alexander Wolff |
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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): | CC BY-NC: Creative-Commons-Lizenz: Namensnennung, Nicht kommerziell |