On embedding a graph in the grid with the minimum number of bends
SIAM Journal on Computing
On the complexity of comparing evolutionary trees
Discrete Applied Mathematics - Special volume on computational molecular biology
An Euler-type formula for median graphs
Discrete Mathematics
Invited Presentation: Median Hulls as Steiner Hulls in Rectilinear and Molecular Sequence Spaces
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
Computing the Hybridization Number of Two Phylogenetic Trees Is Fixed-Parameter Tractable
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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With the number of sequenced genomes growing ever larger, it is now common practice to concatenate sequence alignments from several genomic loci as a first step to phylogenetic tree inference. However, as different loci may support different trees due to processes such as gene duplication and lineage sorting, it is important to better understand how commonly used phylogenetic inference methods behave on such "phylogenetic mixtures". Here we shall focus on how parsimony, one of the most popular methods for reconstructing phylogenetic trees, behaves for mixtures of two trees. In particular, we show that (i) the parsimony problem is NP-complete for mixtures of two trees, (ii) there are mixtures of two trees that have exponentially many (in the number of leaves) most parsimonious trees, and (iii) give an explicit description of the most parsimonious tree(s) and scores corresponding to the mixture of a pair of trees related by a single TBR operation.