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A PolynomialTime Algorithm for the Perfect Phylogeny Problem when the Number of Character States Is Fixed
 SIAM JOURNAL ON COMPUTING
, 1994
"... We present a polynomialtime 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 ..."
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Cited by 51 (2 self)
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We present a polynomialtime 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 NPcomplete in general.
A Fast Algorithm for the Computation and Enumeration of Perfect Phylogenies
 SIAM JOURNAL ON COMPUTING
, 1995
"... 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 NPComplete in general, while the different fixed parameter versions can e ..."
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Cited by 43 (8 self)
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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 NPComplete in general, while the different fixed parameter versions can each be solved in polynomial time. In particular, Agarwala and FernandezBaca have developed an O(2 3r (nk 3 +k 4 )) algorithm for the perfect phylogeny problem for n species defined by k rstate 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...
Fast and simple algorithms for perfect phylogeny and triangulating colored graphs
 INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE
, 1996
"... ..."
A PolynomialTime Algorithm for the Phylogeny Problem when the Number of Character States is Fixed
 SIAM J. COMPUT
, 1993
"... We present a polynomialtime 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 co ..."
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Cited by 6 (0 self)
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We present a polynomialtime 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 NPcomplete in general.
Learning and Approximation Algorithms for problems motivated by Evolutionary Trees
, 1999
"... vi Chapter 1 Introduction 1 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Biological Background . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2.2 Models and Methods . . . . . . ..."
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Cited by 2 (0 self)
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vi Chapter 1 Introduction 1 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Biological Background . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2.2 Models and Methods . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Learning in the General Markov Model . . . . . . . . . . . . . . . 15 1.3.1 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3.2 Learning Problems for Evolutionary Trees . . . . . . . . . 19 1.4 Layout of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Chapter 2 Learning TwoState Markov Evolutionary Trees 28 2.1 Previous research . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.1.1 The General Idea . . . . . . . . . . . . . . . . . . . . . . . . 28 2.1.2 Previous work on learning the distribution . . . . . . . . . 34 2.1.3 Previous work on finding the topology . . . . . . . . . . . . 39 ii 2.1.4 Re...
A Faster Algorithm for the Perfect Phylogeny Problem when the Number of Characters is Fixed
, 1994
"... We present an algorithm for determining whether a set of species, described by the characters they exhibit, has a perfect phylogeny, assuming the maximum number of characters is fixed. This algorithm is simpler and faster than the known algorithms when the number of characters is at least 4. 1 Intro ..."
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We present an algorithm for determining whether a set of species, described by the characters they exhibit, has a perfect phylogeny, assuming the maximum number of characters is fixed. This algorithm is simpler and faster than the known algorithms when the number of characters is at least 4. 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, 10, 11]. Information about evolutionary history can be conveniently represented by an evolutionary or phylogenetic tree, often referred to simply as a phylogeny. In one of the standard models, the problem can be expressed mathematically 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 = (s 1 ; : : : ; s m ) is a vector such that s 2 A 1 \Theta \Delta...
Generalizing the Splits Equivalence Theorem and Four Gamete Condition: Perfect Phylogeny on Three State Characters
"... Abstract. We study the three state perfect phylogeny problem and show that there is a three state perfect phylogeny for a set of input sequences if and only if there is a perfect phylogeny for every subset of three characters. In establishing these results, we prove fundamental structural features o ..."
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Abstract. We study the three state perfect phylogeny problem and show that there is a three state perfect phylogeny for a set of input sequences if and only if there is a perfect phylogeny for every subset of three characters. In establishing these results, we prove fundamental structural features of the perfect phylogeny problem on three state characters and completely characterize the obstruction sets that must occur in input sequences that do not have a perfect phylogeny. We also give a proof for a stated lower bound involved in the conjectured generalization of our main result to any number of states. 1
Proceedings of the Phylogeny Workshop
, 1995
"... 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 rearrang ..."
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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 ...