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

Grafalgo - A Library of Graph Algorithms and Supporting Data Structures (revised)

This report provides an (updated) overview of {\sl Grafalgo}, an open-source library of graph algorithms and the data structures used to implement them. The programs in this library were originally written to support a graduate class in advanced data structures and algorithms at Washington University. Because the code's primary purpose was pedagogical, it was written to be as straightforward as possible, while still being highly efficient. Grafalgo is implemented in C++ and incorporates some features of C++11. The library is available on an open-source basis and may be downloaded from https://code.google.com/p/grafalgo/. Source code documentation is at www.arl.wustl.edu/\textasciitilde jst/doc/grafalgo. While not designed as production code, the library is suitable for use in larger systems, so long as its limitations are understood. The readability of the code also makes it relatively straightforward to extend it for other purposes

Parameterized Approximation Schemes using Graph Widths

Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability of a number of problems which are known to be hard to solve exactly when parameterized by treewidth or clique-width. Our main contribution is to present a natural randomized rounding technique that extends well-known ideas and can be used for both of these widths. Applying this very generic technique we obtain approximation schemes for a number of problems, evading both polynomial-time inapproximability and parameterized intractability bounds