Reconciling taxonomy and phylogenetic inference: formalism and algorithms for describing discord and inferring taxonomic roots

Although taxonomy is often used informally to evaluate the results of phylogenetic inference and find the root of phylogenetic trees, algorithmic methods to do so are lacking. In this paper we formalize these procedures and develop algorithms to solve the relevant problems. In particular, we introduce a new algorithm that solves a "subcoloring" problem for expressing the difference between the taxonomy and phylogeny at a given rank. This algorithm improves upon the current best algorithm in terms of asymptotic complexity for the parameter regime of interest; we also describe a branch-and-bound algorithm that saves orders of magnitude in computation on real data sets. We also develop a formalism and an algorithm for rooting phylogenetic trees according to a taxonomy. All of these algorithms are implemented in freely-available software.Comment: Version submitted to Algorithms for Molecular Biology. A number of fixes from previous versio

A Branch and Bound Algorithm for Exact, Upper, and Lower Bounds on Treewidth

In this paper, a branch and bound algorithm for computing the treewidth of a graph is presented. The method incorporates extensions of existing results, and uses new pruning and reduction rules, based upon roperties of the adopted branching strategy. We discuss how the algorithm can not only be used to obtain exact bounds for the treewidth, but also to obtain upper and/or lower bounds. Computational results of the algorithm are presented

Developing Fixed-Parameter Algorithms to Solve Combinatorially Explosive Biological Problems

Fixed-parameter algorithms can efficiently find optimal solutions to some computationally hard (NP-hard) problems. We survey five main practical techniques to develop such algorithms. Each technique is circumstantiated by case studies of applications to biological problems. We also present other known bioinformatics-related applications and give pointers to experimental results. Key Words: Computationally hard problems; combinatorial explosions; discrete problems; fixed-parameter tractability; optimal solutions.