Dokument-ID Dokumenttyp Verfasser/Autoren Herausgeber Haupttitel Abstract Auflage Verlagsort Verlag Erscheinungsjahr Seitenzahl Schriftenreihe Titel Schriftenreihe Bandzahl ISBN Quelle der Hochschulschrift Konferenzname Quelle:Titel Quelle:Jahrgang Quelle:Heftnummer Quelle:Erste Seite Quelle:Letzte Seite URN DOI Abteilungen OPUS4-12462 Wissenschaftlicher Artikel Buchin, Kevin; Buchin, Maike; Byrka, Jaroslaw; Nöllenburg, Martin; Okamoto, Yoshio; Silveira, Rodrigo I.; Wolff, Alexander 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. 2012 309-332 Algorithmica 62 urn:nbn:de:bvb:20-opus-124622 10.1007/s00453-010-9456-3 Institut für Informatik