title: Reconstructing an ultrametric galled phylogenetic network from a distance matrix.
abstract: Given a distance matrix M that specifies the pairwise evolutionary distances between n species, the phylogenetic tree reconstruction problem asks for an edge-weighted phylogenetic tree that satisfies M, if one exists. We study some extensions of this problem to rooted phylogenetic networks. Our main result is an O(n(2) log n)-time algorithm for determining whether there is an ultrametric galled network that satisfies M, and if so, constructing one. In fact, if such an ultrametric galled network exists, our algorithm is guaranteed to construct one containing the minimum possible number of nodes with more than one parent (hybrid nodes). We also prove that finding a largest possible submatrix M' of M such that there exists an ultrametric galled network that satisfies M' is NP-hard. Furthermore, we show that given an incomplete distance matrix (i.e. where some matrix entries are missing), it is also NP-hard to determine whether there exists an ultrametric galled network which satisfies it.
authors.affiliation: Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong, PR China. hlchan@cs.hku.hk
authors.forename: Ho-Leung
authors.initials: HL
authors.lastname: Chan
authors.forename: Jesper
authors.initials: J
authors.lastname: Jansson
authors.forename: Tak-Wah
authors.initials: TW
authors.lastname: Lam
authors.forename: Siu-Ming
authors.initials: SM
authors.lastname: Yiu
mesh_terms: D000465:Algorithms; D005075:Biological Evolution; D002874:Chromosome Mapping / Q000379:methods*; D003198:Computer Simulation; D019143:Evolution, Molecular; D008957:Models, Genetic; D010802:Phylogeny; D040641:Quantitative Trait Loci / Q000235:genetics*; D017422:Sequence Analysis, DNA / Q000379:methods*