Drawing (complete) binary tanglegrams: hardness, approximation, fixed-parameter tractability

K. Buchin, M. Buchin, J. Byrka, M. Nöllenburg, Y. Okamoto, R.I. Silveira, A. Wolff

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

12 Citaten (Scopus)


A binary tanglegram is a pair of 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 drawing 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 general binary trees. We show that the problem is hard even if both trees are complete binary trees. For this case we give an O(n 3)-time 2-approximation and a new and simple fixed-parameter algorithm. We show that the maximization version of the dual problem for general binary trees can be reduced to a version of MaxCut for which the algorithm of Goemans and Williamson yields a 0.878-approximation.
Originele taal-2Engels
TitelGraph Drawing (16th International Symposium, GD'08, Heraklion, Crete, Greece, September 21-24, 2008, Revised Papers)
RedacteurenI.G. Tollis, M. Patrignani
Plaats van productieBerlin
ISBN van geprinte versie978-3-642-00218-2
StatusGepubliceerd - 2009

Publicatie series

NaamLecture Notes in Computer Science
ISSN van geprinte versie0302-9743

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