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65
A Faster And Simpler Algorithm For Sorting Signed Permutations By Reversals
, 1997
"... We give a quadratictime algorithm for finding the minimum number of reversals needed to sort a signed permutation. Our algorithm is faster than the previous algorithm of Hannenhalli and Pevzner and its faster implementation of Berman and Hannenhalli. The algorithm is conceptually simple and does no ..."
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Cited by 106 (11 self)
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We give a quadratictime algorithm for finding the minimum number of reversals needed to sort a signed permutation. Our algorithm is faster than the previous algorithm of Hannenhalli and Pevzner and its faster implementation of Berman and Hannenhalli. The algorithm is conceptually simple and does not require special data structures. Our study also considerably simplifies the combinatorial structures used by the analysis.
Multiple Genome Rearrangement and Breakpoint Phylogeny
, 1998
"... Multiple alignment of macromolecular sequences generalizes from N = 2 to N # 3 the comparison of N sequences which have diverged through the local processes of insertion, deletion and substitution. Geneorder sequences diverge through nonlocal genome rearrangement processes such as inversion ..."
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Cited by 76 (9 self)
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Multiple alignment of macromolecular sequences generalizes from N = 2 to N # 3 the comparison of N sequences which have diverged through the local processes of insertion, deletion and substitution. Geneorder sequences diverge through nonlocal genome rearrangement processes such as inversion (or reversal) and transposition. In this paper we show which formulations of multiple alignment have counterparts in multiple rearrangement. Based on di#culties inherent in rearrangement editdistance calculation and interpretation, we argue for the simpler "breakpoint analysis ". Consensusbased multiple rearrangement of N # 3 orders can be solved exactly through reduction to instances of the Travelling Salesman Problem (TSP). We propose a branchandbound solution to TSP particularly suited to these instances. Simulations show how nonuniqueness of the solution is attenuated with increasing numbers of data genomes. Treebased multiple alignment can be achieved to a great degree o...
Breakpoint phylogenies
, 1997
"... We describe a number of heuristics for inferring the gene orders of the hypothetical ancestral genomes in a fixed phylogeny. The optimization criterion is the minimum number of breakpoints (pairs of genes adjacent in one genome but not the other) in the gene orders of two genomes connected byanedge ..."
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Cited by 59 (4 self)
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We describe a number of heuristics for inferring the gene orders of the hypothetical ancestral genomes in a fixed phylogeny. The optimization criterion is the minimum number of breakpoints (pairs of genes adjacent in one genome but not the other) in the gene orders of two genomes connected byanedge of the tree, summed over all edges. The key to the method is an exact solution for trees with three leaves (the median problem) based on a reduction to the Traveling Salesman Problem.
Sorting Permutations by Reversals and Eulerian Cycle Decompositions
 SIAM Journal on Discrete Mathematics
, 1997
"... We analyze the strong relationship among three combinatorial problems, namely the problem of sorting a permutation by the minimum number of reversals (MINSBR), the problem of finding the maximum number of edgedisjoint alternating cycles in a breakpoint graph associated with a given permutation (MA ..."
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Cited by 54 (9 self)
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We analyze the strong relationship among three combinatorial problems, namely the problem of sorting a permutation by the minimum number of reversals (MINSBR), the problem of finding the maximum number of edgedisjoint alternating cycles in a breakpoint graph associated with a given permutation (MAXACD), and the problem of partitioning the edge set of a Eulerian graph into the maximum number of cycles (MAXECD). We first illustrate a nice characterization of breakpoint graphs, which leads to a linear time algorithm for their recognition. This characterization is used to prove that MAXECD and MAXACD are equivalent, showing the latter is NPhard. We then describe a transformation from MAXACD to MINSBR, which is therefore shown to be NPhard as well, answering an outstanding question which has been open for some years. Finally, we derive the worstcase performance of a well known lower bound for MINSBR, obtained by solving MAXACD, discussing its implications on approximation algori...
The Median Problem for Breakpoints in Comparative Genomics
, 1997
"... During evolution, chromosomal rearrangements, such as reciprocal translocation, transposition and inversion, disrupt gene content and gene order on chromosomes. We discuss algorithmic and statistical approaches to the analysis of comparative genomic data. In a phylogenetic context, a combined ap ..."
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Cited by 41 (12 self)
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During evolution, chromosomal rearrangements, such as reciprocal translocation, transposition and inversion, disrupt gene content and gene order on chromosomes. We discuss algorithmic and statistical approaches to the analysis of comparative genomic data. In a phylogenetic context, a combined approach is suggested, leading to the median problem for breakpoints.
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 39 (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...
Of mice and men: Algorithms for evolutionary distances between genomes with translocation
, 1995
"... A new and largely unexplored area of computational biology is combinatorial algorithms for genome rearrangement. In the course of its evolution, the genome of an organism mutates by processes that can rearrange whole segments of a chromosome in a single event. These rearrangement mechanisms include ..."
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Cited by 25 (1 self)
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A new and largely unexplored area of computational biology is combinatorial algorithms for genome rearrangement. In the course of its evolution, the genome of an organism mutates by processes that can rearrange whole segments of a chromosome in a single event. These rearrangement mechanisms include inversion, transposition, duplication, and translocation, and a basic problem is to determine the minimum number of such events that transform one genome to another. This number is called the rearrangement distance between the two genomes, and gives a lower bound on the number of events that must have occurred since their divergence, assuming evolution proceeds according to the processes of the study. In this paper, we begin the algorithmic study of genome rearrangement by translocation. A translocation exchanges material at the end of two chromosomes within a genome. We model this as a process that exchanges prefixes and suffixes of strings, where each string represents a sequence of distin...
On the Complexity and Approximation of Syntenic Distance
, 1998
"... The paper studies the computational complexity and approximation algorithms for a new evolutionary distance between multichromosomal genomes introduced recently by Ferretti, Nadeau and Sankoff. Here, a chromosome is represented as a set of genes and a genome is a collections of chromosomes. The syn ..."
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Cited by 15 (1 self)
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The paper studies the computational complexity and approximation algorithms for a new evolutionary distance between multichromosomal genomes introduced recently by Ferretti, Nadeau and Sankoff. Here, a chromosome is represented as a set of genes and a genome is a collections of chromosomes. The syntenic distance between two genomes is defined as the minimum number of translocations, fusions and fissions required to transform one genome into the other. We prove that computing the syntenic distance is NPhard and give a simple approximation algorithm with performance ratio 2. For the case when an upper bound d on the syntenic distance is known, we show that an an optimal syntenic sequence can be found in O(nk + 2 O(d 2 ) ) time, where n and k are the number of chromosomes in the two given genomes. Next, we show that if the set of operations for transforming a genome is significantly restricted, we can nevertheless find a solution that performs at most O(logd) additional moves, wher...
Steiner Points in the Space of Genome Rearrangements
, 1996
"... We present some experiences with the problem of multiple genome comparison, analogous to multiple sequence alignment in sequence comparison, under the inversion and transposition distance metrics, given a fixed phylogeny. We first describe a heuristic for the case in which phylogeny is a star on thr ..."
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Cited by 14 (2 self)
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We present some experiences with the problem of multiple genome comparison, analogous to multiple sequence alignment in sequence comparison, under the inversion and transposition distance metrics, given a fixed phylogeny. We first describe a heuristic for the case in which phylogeny is a star on three vertices and then use this to approximate the multiple genome comparison problem via local search. Keywords Permutation reversals, chromosome inversions, median problem, phylogeny 1 Introduction Although the mathematical nature of the problems are very different, genome comparison has inherited much of the spirit of traditional research into sequence comparison. This paper explores the concept of multiple genome comparison, analogous to multiple sequence alignment in sequence comparison. And just as the original multiple alignment problem [17] was posed in terms of optimizing the internal nodes of a given phylogenetic tree by minimizing the sum of an edit distance over the branches of th...
Opportunities for Combinatorial Optimization In Computational Biology
, 2003
"... This is a survey designed for mathematical programming people who do not know molecular biology and want to learn the kinds of combinatorial optimization problems that arise. After a brief introduction to the biology, we present optimization models pertaining to sequencing, evolutionary explanations ..."
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Cited by 14 (0 self)
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This is a survey designed for mathematical programming people who do not know molecular biology and want to learn the kinds of combinatorial optimization problems that arise. After a brief introduction to the biology, we present optimization models pertaining to sequencing, evolutionary explanations, structure prediction and recognition. Additional biology is given in the context of the problems, including some motivation for disease diagnosis and drug discovery. Open problems are cited with an extensive bibliography, and we o er a guide to getting started in this exciting frontier.