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29
Transforming Cabbage into Turnip (polynomial algorithm for sorting signed permutations by reversals)
 Journal of the ACM
, 1995
"... Analysis of genome rearrangements in molecular biology started in the late 1930's, when Dobzhansky and Sturtevant published a milestone paper presenting a rearrangement scenario with 17 inversions for the species of Drosophila. Analysis of genomes evolving by inversions leads to a combinatorial pro ..."
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Cited by 273 (9 self)
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Analysis of genome rearrangements in molecular biology started in the late 1930's, when Dobzhansky and Sturtevant published a milestone paper presenting a rearrangement scenario with 17 inversions for the species of Drosophila. Analysis of genomes evolving by inversions leads to a combinatorial problem of sorting by reversals studied in detail recently. Kececioglu and Sankoff conjectured that sorting by reversals is NPhard, but despite many attempts their conjecture remains open. We study sorting of signed permutations by reversals, a problem which adequately models rearrangements in small genomes like chloroplast or mitochondrial DNA. The previously suggested performance guarantee algorithms for sorting signed permutations by reversals approximate the reversal distance between permutations with an astonishing accuracy for both simulated and biological data. We prove a duality theorem explaining this intriguing performance and show that there exists a "hidden" parameter which allow...
Optimal, efficient reconstruction of phylogenetic networks with constrained recombination
 J. Bioinformatics and Computational Biology
, 2003
"... gusfield,eddhu¡ A phylogenetic network is a generalization of a phylogenetic tree, allowing structural properties that are not treelike. With the growth of genomic data, much of which does not fit ideal tree models, there is greater need to understand the algorithmics and combinatorics of phylogenet ..."
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Cited by 94 (13 self)
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gusfield,eddhu¡ A phylogenetic network is a generalization of a phylogenetic tree, allowing structural properties that are not treelike. With the growth of genomic data, much of which does not fit ideal tree models, there is greater need to understand the algorithmics and combinatorics of phylogenetic networks [10, 11]. However, to date, very little has been published on this, with the notable exception of the paper by Wang et al.[12]. Other related papers include [4, 5, 7] We consider the problem introduced in [12], of determining whether the sequences can be derived on a phylogenetic network where the recombination cycles are node disjoint. In this paper, we call such a phylogenetic network a “galledtree”. By more deeply analysing the combinatorial constraints on cycledisjoint phylogenetic networks, we obtain an efficient algorithm that is guaranteed to be both a necessary and sufficient test for the existence of a galledtree for the data. If there is a galledtree, the algorithm constructs one and obtains an implicit representation of all the galled trees for the data, and can create these in linear time for each one. We also note two additional results related to galled trees: first, any set of sequences that can be derived on a galled tree can be derived on a true tree (without recombination cycles), where at most one back mutation is allowed per site; second, the site compatibility problem (which is NPhard in general) can be solved in linear time for any set of sequences that can be derived on a galled tree. The combinatorial constraints we develop apply (for the most part) to nodedisjoint cycles in any phylogenetic network (not just galledtrees), and can be used for example to prove that a given site cannot be on a nodedisjoint cycle in any phylogenetic network. Perhaps more important than the specific results about galledtrees, we introduce an approach that can be used to study recombination in phylogenetic networks that go beyond galledtrees.
Transforming men into mice (polynomial algorithm for genomic distance problem
 In 36th Annual IEEE Symposium on Foundations of Computer Science
, 1995
"... Then Puss said, \I understand that you have magical powers, that you can change yourself into any kind of animal... But, it must be easy to turn yourself into something huge. However, it must be impossible to turn into something very, very small like a mouse". Brothers Grimm, Puss N Boots Many ..."
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Cited by 83 (9 self)
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Then Puss said, \I understand that you have magical powers, that you can change yourself into any kind of animal... But, it must be easy to turn yourself into something huge. However, it must be impossible to turn into something very, very small like a mouse". Brothers Grimm, Puss N Boots Many people (including ourselves) believe that transformations of humans into mice happen only in fairy tales. However, despite some di erences in appearance and habits, men and mice are genetically very similar. In the pioneering paper, Nadeau and Taylor, 1984 estimated that surprisingly few genomic rearrangements (178 39) happened since the divergence of human and mouse 80 million years ago. However, their analysis is nonconstructive and no rearrangement scenario for humanmouse evolution has been suggested yet. The problem is complicated by the fact that rearrangements in multichromosomal genomes include inversions, translocations, fusions and ssions of chromosomes, a rather complex set of operations. As a result, at the rst glance, a polynomial algorithm for the genomic distance problem with all these operations looks almost as improbable as the transformation of a (real) man into a (real) mouse. We prove a duality theorem which expresses the genomic distance in terms of easily computable parameters re ecting di erent combinatorial properties of sets of strings. This theorem leads to a polynomialtime algorithm for computing most parsimonious rearrangement scenarios. Based on this result and the latest comparative physical mapping data we have constructed a scenario of humanmouse evolution with 131 reversals/translocations/fusions / ssions. Acombination of the genome rearrangement algorithm with the recently proposed experimental technique called ZOOFISH suggests a new constructive approach to the 100year old problem of reconstructing mammalian evolution.
On the Complexity of Comparing Evolutionary Trees
, 1995
"... We study the computational complexity and approximation of several problems arising in the comparison of evolutionary trees. It is shown that the maximum agreement subtree (MAST) problem for three trees with unbounded degree cannot be approximated within ratio 2 log n in polynomial time for any ..."
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Cited by 58 (8 self)
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We study the computational complexity and approximation of several problems arising in the comparison of evolutionary trees. It is shown that the maximum agreement subtree (MAST) problem for three trees with unbounded degree cannot be approximated within ratio 2 log n in polynomial time for any < 1, unless NP DTIME[2 polylog n ], and MAST with edge contractions for two binary trees is NPhard. This answers two open questions posed in [1]. For the maximum renement subtree (MRST) problem involving two trees, we show that it is polynomialtime solvable when both trees have bounded degree and is NPhard when one of the trees can have an arbitrary degree. Finally, we consider the problem of optimally transforming a tree into another by transferring subtrees around. It is shown that computing the subtreetransfer distance is NPhard and an approximation algorithm with performance ratio 3 is given. Key words: Evolutionary tree, phylogeny, compatibility, recombination, computational c...
Fast Sorting by Reversal
, 1996
"... Analysis of genomes evolving by inversions leads to a combinatorial problem of sorting by reversals studied in detail recently. Following a series of work recently, Hannenhalli and Pevzner developed the first polynomial algorithm for the problem of sorting signed permutations by reversals and propos ..."
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Cited by 52 (3 self)
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Analysis of genomes evolving by inversions leads to a combinatorial problem of sorting by reversals studied in detail recently. Following a series of work recently, Hannenhalli and Pevzner developed the first polynomial algorithm for the problem of sorting signed permutations by reversals and proposed an O(n 4 ) implementation of the algorithm. In this paper we exploit a few combinatorial properties of the cycle graph of a permutation and propose an O(n 2 ff(n)) implementation of the algorithm where ff is the inverse Ackerman function. Besides making this algorithm practical, our technique improves implementations of the other rearrangement distance problems. 3 This work is supported by NSF grant CCR9114545. 4 This work is supported by NSF Young Investigator Award, NIH grant 1R01 HG00987 and DOE grant DEFG0294ER61919. (turnip) (cabbage) 1 2 3 4 5 23 45 1 15 43 2 23 45 1 B. oleracea B. campestris Figure 1: "Transformation" of cabbage into turnip 1 Introduction In th...
A Fundamental Decomposition Theory for Phylogenetic Networks and Incompatible Characters
 In proc Research in Computational Molecular Biology
, 2005
"... ..."
1.375Approximation Algorithm for Sorting by Reversals
, 2001
"... Analysis of genomes evolving by inversions leads to a general combinatorial problem of Sorting by Reversals, MINSBR, the problem of sorting a permutation by a minimum number of reversals. This combinatorial problem has a long history, and a number of other motivations. It was studied in a great ..."
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Cited by 37 (1 self)
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Analysis of genomes evolving by inversions leads to a general combinatorial problem of Sorting by Reversals, MINSBR, the problem of sorting a permutation by a minimum number of reversals. This combinatorial problem has a long history, and a number of other motivations. It was studied in a great detail recently in computational molecular biology. Following a series of preliminary results, Hannenhalli and Pevzner developed the first exact polynomial time algorithm for the problem of sorting signed permutations by reversals, and a polynomial time algorithm for a special case of unsigned permutations. The best known approximation algorithm for MINSBR, due to Christie, gives a performance ratio of 1.5. In this paper, by exploiting the polynomial time algorithm for sorting signed permutations and by developing a new approximation algorithm for maximum cycle decomposition of breakpoint graphs, we improve the performance ratio for MINSBR to 1.375.
Efficient computation of close lower and upper bounds on the minimum number of needed recombinations in the evolution of biological sequences
 Bioinformatics
, 2005
"... or population genetics ..."
Methods for inferring blockwise ancestral history from haploid sequences: The haplotype coloring problem
 In Lecture Notes in Computer Science 2452 (Proceedings of the Second International Workshop on Algorithms in Bioinformatics
, 2002
"... Abstract. Recent evidence for a “blocky ” haplotype structure to the human genome and for its importance to disease inference studies has created a pressing need for tools that identify patterns of past recombination in sequences of samples of human genes and gene regions. We present two new approac ..."
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Cited by 17 (6 self)
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Abstract. Recent evidence for a “blocky ” haplotype structure to the human genome and for its importance to disease inference studies has created a pressing need for tools that identify patterns of past recombination in sequences of samples of human genes and gene regions. We present two new approaches to the reconstruction of likely recombination patterns from a set of haploid sequences which each combine combinatorial optimization techniques with statistically motivated recombination models. The first breaks the problem into two discrete steps: finding recombination sites then coloring sequences to signify the likely ancestry of each segment. The second poses the problem as optimizing a single probability function for parsing a sequence in terms of ancestral haplotypes. We explain the motivation for each method, present algorithms, show their correctness, and analyze their complexity. We illustrate and analyze the methods with results on real, contrived, and simulated datasets. 1
Finding founder sequences from a set of recombinants
 In Lecture
"... Abstract. Inspired by the current interest in the so–called haplotype blocks we consider a related, complementary problem abstracted from the following scenario. We are given the DNA or SNP sequences of a sample of individuals from a (human) population. The population is assumed to have evolved as a ..."
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Cited by 16 (3 self)
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Abstract. Inspired by the current interest in the so–called haplotype blocks we consider a related, complementary problem abstracted from the following scenario. We are given the DNA or SNP sequences of a sample of individuals from a (human) population. The population is assumed to have evolved as an isolate, founded some generations ago by a relatively small number of settlers. Then the sequences in our given sample should be a result of recombinations of the corresponding sequences of the founders, possibly corrupted by (rare) point mutations. We are interested in finding plausible reconstructions of the sequences of the founders. Formulated as a combinatorial string problem, one has to find a set of founder sequences such that given sequences can be composed from fragments taken from the corresponding locations of the founder sequences. The solution can be optimized for example with respect to the number of founders or the number of crossovers. We give polynomial– time algorithms for some special cases as well as a general solution by dynamic programming. 1