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62
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 49 (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...
IndoEuropean and Computational Cladistics
, 2002
"... This paper reports the results of an attempt to recover the ®rstorder subgrouping of the IndoEuropean family using a new computational method devised by the authors and based on a `perfect phylogeny' algorithm. The methodology is also brie¯y described, and points of theory and methodology are ..."
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Cited by 44 (7 self)
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This paper reports the results of an attempt to recover the ®rstorder subgrouping of the IndoEuropean family using a new computational method devised by the authors and based on a `perfect phylogeny' algorithm. The methodology is also brie¯y described, and points of theory and methodology are addressed in connection with the experiment whose results are here reported.
Reconstructing a History of Recombinations From a Set of Sequences
 Discrete Appl. Math
, 1998
"... One of the classic problems in computational biology is the reconstruction of evolutionary history. A recent trend in the area is to increase the explanatory power of the models that are considered by incorporating higherorder evolutionary events that more accurately reflect the mechanisms of mutat ..."
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Cited by 38 (6 self)
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One of the classic problems in computational biology is the reconstruction of evolutionary history. A recent trend in the area is to increase the explanatory power of the models that are considered by incorporating higherorder evolutionary events that more accurately reflect the mechanisms of mutation at the level of the chromosome. We take a step in this direction by considering the problem of reconstructing an evolutionary history for a set of genetic sequences that have evolved by recombination. Recombination is a nontreelike event that produces a child sequence by crossing two parent sequences. We present polynomialtime algorithms for reconstructing a parsimonious history of such events for several models of recombination when all sequences, including those of ancestors, are present in the input. We also show that these models appear to be near the limit of what can be solved in polynomial time, in that several natural generalizations are NPcomplete. Keywords Computational bio...
Faster Exact Algorithms for Hard Problems: A Parameterized Point of View
 Discrete Mathematics
, 2000
"... Recent times have seen quite some progress in the development of "efficient" exponential time algorithms for NPhard problems. These results are also tightly related to the socalled theory of fixed parameter tractability. In this incomplete, personally biased survey, we reflect on some re ..."
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Cited by 30 (4 self)
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Recent times have seen quite some progress in the development of "efficient" exponential time algorithms for NPhard problems. These results are also tightly related to the socalled theory of fixed parameter tractability. In this incomplete, personally biased survey, we reflect on some recent developments and prospects in the field of fixed parameter algorithms.
Incomplete directed perfect phylogeny
 Siam Journal of Computing
, 2000
"... Abstract. Perfect phylogeny is one of the fundamental models for studying evolution. We investigate the following generalization of the problem: The input is a speciescharacters matrix. The characters are binary and directed, i.e., a species can only gain characters. The difference from standard pe ..."
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Cited by 26 (2 self)
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Abstract. Perfect phylogeny is one of the fundamental models for studying evolution. We investigate the following generalization of the problem: The input is a speciescharacters matrix. The characters are binary and directed, i.e., a species can only gain characters. The difference from standard perfect phylogeny is that for some species the state of some characters is unknown. The question is whether one can complete the missing states in a way admitting a perfect phylogeny. The problem arises in classical phylogenetic studies, when some states are missing or undetermined. Quite recently, studies that infer phylogenies using inserted repeat elements in DNA gave rise to the same problem. The best known algorithm for the problem requires O(n2m) time for m characters and n species. We provide a near optimal ~O(nm)time algorithm for the problem. 1 Introduction When studying evolution, the divergence patterns leading from a single ancestor species to its contemporary descendants are usually modeled by a tree structure. Extant species correspond to the tree leaves, while their common progenitor corresponds to the root of this phylogenetic tree. Internal nodes correspond to hypothetical ancient species, which putatively split up and evolved into distinct species. Tree branches model changes through time of the hypothetical ancestor species. The common case is that one has information regarding the leaves, from which the phylogenetic tree is to be inferred. This task, called phylogenetic reconstruction (cf. [7]), was one of the first algorithmic challenges posed by biology, and the computational community has been dealing with problems of this flavor for over three decades (see, e.g., [12]). In the characterbased approach to tree reconstruction, contemporary species are described by their attributes or characters. Each character takes on one of several possible states. The input is represented by a matrix A where aij is the state of character j in species i, and the ith row is the character vector of species i. The output sought is a hypothesis regarding evolution, i.e., a phylogenetic tree along with the suggested charactervectors of the internal nodes. This output must satisfy properties specified by the problem variant.
Fast and simple algorithms for perfect phylogeny and triangulating colored graphs
 INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE
, 1996
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Fixed parameter tractability of binary nearperfect phylogenetic tree reconstruction
 International Colloquium on Automata, Languages and Programming
, 2006
"... Abstract. We consider the problem of finding a Steiner minimum tree in a hypercube. Specifically, given n terminal vertices in an m dimensional cube and a parameter q, we compute the Steiner minimum tree in time O(72 q + 8 q nm 2), under the assumption that the length of the minimum Steiner tree is ..."
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Cited by 18 (7 self)
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Abstract. We consider the problem of finding a Steiner minimum tree in a hypercube. Specifically, given n terminal vertices in an m dimensional cube and a parameter q, we compute the Steiner minimum tree in time O(72 q + 8 q nm 2), under the assumption that the length of the minimum Steiner tree is at most m + q. This problem has extensive applications in taxonomy and biology. The Steiner tree problem in hypercubes is equivalent to the phylogeny (evolutionary tree) reconstruction problem under the maximum parsimony criterion, when each taxon is defined over binary states. The taxa, character set and mutation of a phylogeny correspond to terminal vertices, dimensions and traversal of a dimension in a Steiner tree. Phylogenetic trees that mutate each character exactly once are called perfect phylogenies and their size is bounded by the number of characters. When a perfect phylogeny consistent with the data set exists it can be constructed in linear time. However, real data sets often do not admit perfect phylogenies. In this paper, we consider the problem of reconstructing nearperfect phylogenetic trees (referred to as BNPP). A nearperfect phylogeny relaxes the perfect phylogeny assumption by allowing at most q additional mutations. We show for the first time that the BNPP problem is fixed parameter tractable (FPT) and significantly improve the previous asymptotic bounds. 1
The Hardness of Perfect Phylogeny, Feasible Register Assignment and Other Problems on Thin Colored Graphs
"... In this paper, we consider the complexity of a number of combinatorial problems; namely, Intervalizing Colored Graphs (DNA physical mapping), Triangulating Colored Graphs (perfect phylogeny), (Directed) (Modified) Colored Cutwidth, Feasible Register Assignment and Module Allocation for graphs of bou ..."
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Cited by 18 (4 self)
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In this paper, we consider the complexity of a number of combinatorial problems; namely, Intervalizing Colored Graphs (DNA physical mapping), Triangulating Colored Graphs (perfect phylogeny), (Directed) (Modified) Colored Cutwidth, Feasible Register Assignment and Module Allocation for graphs of bounded pathwidth. Each of these problems has as a characteristic a uniform upper bound on the tree or path width of the graphs in "yes"instances. For all of these problems with the exceptions of Feasible Register Assignment and Module Allocation, a vertex or edge coloring is given as part of the input. Our main results are that the parameterized variant of each of the considered problems is hard for the complexity classes W [t] for all t 2 N. We also show that Intervalizing Colored Graphs, Triangulating Colored Graphs, and Colored Cutwidth are NPComplete. 1 Introduction This paper focuses on a number of graph decision problems which share the characteristic that all have a uniform upper bo...
Better Methods for Solving Parsimony and Compatibility
 Journal of Computational Biology
, 1998
"... Evolutionary tree reconstruction is a challenging problem with important applications in Biology and Linguistics. In Biology, one of the most promising approaches to tree reconstruction is to find the "maximum parsimony" tree, while in Linguistics, the use of the "maximum ..."
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Cited by 15 (3 self)
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Evolutionary tree reconstruction is a challenging problem with important applications in Biology and Linguistics. In Biology, one of the most promising approaches to tree reconstruction is to find the "maximum parsimony" tree, while in Linguistics, the use of the "maximum