Efficient FPT Algorithms for (Strict) Compatibility of Unrooted Phylogenetic Trees

Bull Math Biol. 2017 Apr;79(4):920-938. doi: 10.1007/s11538-017-0260-y. Epub 2017 Feb 28.


In phylogenetics, a central problem is to infer the evolutionary relationships between a set of species X; these relationships are often depicted via a phylogenetic tree-a tree having its leaves labeled bijectively by elements of X and without degree-2 nodes-called the "species tree." One common approach for reconstructing a species tree consists in first constructing several phylogenetic trees from primary data (e.g., DNA sequences originating from some species in X), and then constructing a single phylogenetic tree maximizing the "concordance" with the input trees. The obtained tree is our estimation of the species tree and, when the input trees are defined on overlapping-but not identical-sets of labels, is called "supertree." In this paper, we focus on two problems that are central when combining phylogenetic trees into a supertree: the compatibility and the strict compatibility problems for unrooted phylogenetic trees. These problems are strongly related, respectively, to the notions of "containing as a minor" and "containing as a topological minor" in the graph community. Both problems are known to be fixed parameter tractable in the number of input trees k, by using their expressibility in monadic second-order logic and a reduction to graphs of bounded treewidth. Motivated by the fact that the dependency on k of these algorithms is prohibitively large, we give the first explicit dynamic programming algorithms for solving these problems, both running in time [Formula: see text], where n is the total size of the input.

Keywords: Compatibility; Dynamic programming; FPT algorithm; Parameterized complexity; Phylogenetics; Unrooted phylogenetic trees.

MeSH terms

  • Algorithms*
  • Base Sequence
  • Biological Evolution*
  • Models, Genetic
  • Phylogeny*