We present a polynomial-time algorithm for determining whether a set of species, described by the characters they exhibit, has a perfect phylogeny, assuming the maximum number of possible states for a character is fixed. This solves a longstanding open problem. Our result should be contrasted with the proof by Steel and Bodlaender, Fellows, and Warnow that the perfect phylogeny problem is NP-complete in general.

The Perfect Phylogeny Problem is a classical problem in computational evolutionary biology, in which a set of species/taxa is described by a set of qualitative characters. In recent years, the problem has been shown to be NP-Complete in general, while the different fixed parameter versions can each be solved in polynomial time. In particular, Agarwala and Fernandez-Baca have developed an O(2 3r (nk 3 +k 4 )) algorithm for the perfect phylogeny problem for n species defined by k r-state characters. Since commonly the character data is drawn from alignments of molecular sequences, k is the length of the sequences and can thus be very large (in the hundreds or thousands). Thus, it is imperative to develop algorithms which run efficiently for large values of k. In this paper we make additional observations about the structure of the problem and produce an algorithm for the problem that runs in time O(2 2r k 2 n). We also show how it is possible to efficiently build a...

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We present a polynomial-time algorithm for determining whether a set of species, described by the characters they exhibit, has a phylogenetic tree, assuming the maximum number of possible states for a character is fixed. This solves an open problem posed by Kannan and Warnow. Our result should be contrasted with the proof by Steel and Bodlaender, Fellows, and Warnow that the phylogeny problem is NP-complete in general. 1 Introduction A fundamental problem in biology is that of inferring the evolutionary history of a set of species, each of which is specified by the set of traits or characters that it exhibits [6, 7]. In mathematical terms, the problem can be expressed as follows. Let C = f1; : : : ; mg be the character set, and for every c 2 C, let A c = f1; : : : ; r c g be the set of allowable states for character c. We write r to denote max c2C r c . A species s is a vector (s 1 ; : : : ; s m ) such that s 2 A 1 \Theta \Delta \Delta \Delta \Theta Am ; s c is referred to as the st...

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Sequence comparison in computational molecular biology is a powerful tool for deriving evolutionary and functional relationships between genes. However, classical alignment algorithms handle only local mutations (i.e. insertions, deletions and substitutions of nucleotides) and ignore global rearrangements (i.e. inversions and transpositions of long fragments). As a result, applications of sequence alignment in analyzing highly rearranged genomes (i.e. herpes viruses or plant mitochondrial DNA) are very limited and may lead to contradictions in molecular phylogeny studies since different genes give rise to different evolutionary trees. The paper describes the problem of genome comparison versus classical gene comparison and presents algorithms to analyze rearrangements in genomes evolving by inversions. In the simplest form the problem corresponds to sorting by reversals, i.e. sorting of an array using reversals of arbitrary fragments. We describe algorithms to analyze genomes evolving ...

this paper we will show that a well-known set of controversies in historical linguistics can be resolved by a new tree-construction methodology combining ideas from biology, techniques from computer science, and scholarship in historical linguistics. A problem that has generated controversy in historical linguistics for more than a century is finding the correct evolutionary tree for the Indo-European (IE) family of languages. The existence and membership of the family are not in doubt; neither is the fact that there are ten subfamilies of IE that include languages still spoken or adequately recorded. (There seem to be a few more that include extinct languages very sparsely recorded, but we must leave them aside for sheer lack of evidence.) But if you look at a "traditional family tree" of IE, it will show all ten major subgroups evolving independently from the ancestor language, Proto-Indo-European (PIE; see fig.1) and that cannot possibly be correct, if only because the simultaneous ten-way speciation of a single language community is almost unimaginable under neolithic conditions. What a tree like this really indicates is that specialists cannot determine the correct first-order branching of the tree using traditional methods. In fact, while historical linguistics has long had a limited but highly reliable method for evaluating evolutionary trees, it has never had a rigorous method for constructing all the optimal evolutionary trees for a language family (by any measure of optimality). 2 Lessons from biology