Drawing (Complete) Binary Tanglegrams
Zitieren Sie bitte immer diese 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.…
Autor(en): | 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 |
Dokumentart: | Artikel / Aufsatz in einer Zeitschrift |
Institute der Universität: | Fakultät für Mathematik und Informatik / Institut für Informatik |
Sprache der Veröffentlichung: | Englisch |
Titel des übergeordneten Werkes / der Zeitschrift (Englisch): | Algorithmica |
Erscheinungsjahr: | 2012 |
Band / Jahrgang: | 62 |
Seitenangabe: | 309-332 |
Originalveröffentlichung / Quelle: | Algorithmica (2012) 62:309–332. doi:10.1007/s00453-010-9456-3 |
DOI: | https://doi.org/10.1007/s00453-010-9456-3 |
Allgemeine fachliche Zuordnung (DDC-Klassifikation): | 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik |
Freie Schlagwort(e): | NP-hardness; approximation algorithm; binary tanglegram; crossing minimization; fixed-parameter tractability |
Datum der Freischaltung: | 20.01.2016 |
Lizenz (Deutsch): | CC BY-NC: Creative-Commons-Lizenz: Namensnennung, Nicht kommerziell |