The complexity of deriving multi-labeled trees from bipartitions

Katharina T. Huber, Martin Lott, Vincent Moulton, Andreas Spillner

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


Recently, multi-labeled trees have been used to help unravel the evolutionary origins of polyploid species. A multi-labeled tree is the same as a phylogenetic tree except that more than one leaf may be labeled by a single species, so that the leaf set of a multi-labeled tree can be regarded as a multiset. In contrast to phylogenetic trees, which can be efficiently encoded in terms of certain bipartitions of their leaf sets, we show that it is NP-hard to decide whether a collection of bipartitions of a multiset can be represented by a multi-labeled tree. Even so, we also show that it is possible to generalize to multi-labeled trees a well-known condition that characterizes when a collection of bipartitions encodes a phylogenetic tree. Using this generalization, we obtain a fixed-parameter algorithm for the above decision problem in terms of a parameter associated to the given multiset.
Original languageEnglish
Pages (from-to)639-651
Number of pages13
JournalJournal of Computational Biology
Issue number6
Publication statusPublished - 2008

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