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## Sorting with Fixed-Length Reversals (1996)

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Venue: | Discrete Applied Mathematics |

Citations: | 15 - 1 self |

### Citations

203 |
Genome rearrangements and sorting by reversals
- Bafna, Pevzner
- 1993
(Show Context)
Citation Context ...plied, for example, to drosophila [8, 21], plants [4, 18], viruses [12], and mammals [7, 20]. Kececloglu and Sankoff [16] gave 2-approximation algorithms on reversal distance, which Bafna and Pevzner =-=[3]-=- improved to a factor of 7/4 approximation. Most recently, Hannenhalli and Pevzner [11] gave a polynomial-time algorithm for signed reversal distance, although the problem for unsigned reversals (as w... |

140 | Sorting by transpositions.
- Bafna, Pevzner
- 1998
(Show Context)
Citation Context ...d reversals (as we consider in this paper) remains open. Kececloglu and Sankoff [17] report on the success of heuristics and search in determining reversal distance for chromosomes. Bafna and Pevzner =-=[5]-=- present approximation algorithms for transposition distance, ie. under block moves instead of reversals. All of these problems are special cases of determining the diameter of permutation groups. Jer... |

118 |
Lengths of chromosomal segments conserved since divergence of man and mouse.
- Nadeau, Taylor
- 1984
(Show Context)
Citation Context ...ting one genome to another corresponds to the most likely evolutionary path between them. This analysis has been applied, for example, to drosophila [8, 21], plants [4, 18], viruses [12], and mammals =-=[7, 20]-=-. Kececloglu and Sankoff [16] gave 2-approximation algorithms on reversal distance, which Bafna and Pevzner [3] improved to a factor of 7/4 approximation. Most recently, Hannenhalli and Pevzner [11] g... |

70 |
The Art of Computer Programming, vol III { Sorting and Searching
- Knuth
- 1973
(Show Context)
Citation Context ...ting with (n \Gamma k)-reversals. Previous work on sorting with fixed-length reversals has focused on the special case where k = 2. Thus each reversal simply transposes adjacent elements. Bubble sort =-=[19] sorts a-=-ny permutation �� using exactly one transposition for each inversion in ��, thus minimizing the number of reversals. Jerrum [15] presented a polynomial algorithm for the much more difficult pr... |

64 | Polynomial algorithm for computing translocation distance between genomes
- Hannenhalli
- 1995
(Show Context)
Citation Context ...7, 20]. Kececloglu and Sankoff [16] gave 2-approximation algorithms on reversal distance, which Bafna and Pevzner [3] improved to a factor of 7/4 approximation. Most recently, Hannenhalli and Pevzner =-=[11]-=- gave a polynomial-time algorithm for signed reversal distance, although the problem for unsigned reversals (as we consider in this paper) remains open. Kececloglu and Sankoff [17] report on the succe... |

64 |
The chromosome inversion problem.
- Watterson, Ewens, et al.
- 1982
(Show Context)
Citation Context ...cience State University of New York Stony Brook, NY 11794-4400 ftichen,skienag@cs.sunysb.edu March 25, 1996 1 Introduction Due to applications in reconstructing the evolutionary history of the genome =-=[22]-=- and to the design of interconnection networks [14], there has been considerable recent interest in problems of sorting permutations with reversals. In this paper, we study the problem of sorting perm... |

63 | Bounds for sorting by prefix reversal,
- GATES, PAPADIMITRIOU
- 1979
(Show Context)
Citation Context ...umber of reversals. Jerrum [15] presented a polynomial algorithm for the much more difficult problem of sorting circular permutations using a minimum number of transpositions. Gates and Papadimitriou =-=[9]-=- (also [10]) studied the problem of sorting permutations using prefix reversals (better known as the pancake-flipping problem), where reversals may be of arbitrary length but each must start from the ... |

57 | Exact and approximation algorithms for the inversion distance.
- Kececioglu, Sanko
- 1995
(Show Context)
Citation Context ...sponds to the most likely evolutionary path between them. This analysis has been applied, for example, to drosophila [8, 21], plants [4, 18], viruses [12], and mammals [7, 20]. Kececloglu and Sankoff =-=[16]-=- gave 2-approximation algorithms on reversal distance, which Bafna and Pevzner [3] improved to a factor of 7/4 approximation. Most recently, Hannenhalli and Pevzner [11] gave a polynomial-time algorit... |

52 | Sorting by reversals: Genome rearrangement in plant organelles and evolutionary history of X chromosome
- Bafna, Pevzner
- 1995
(Show Context)
Citation Context ...s. A shortest reversal sequence sorting one genome to another corresponds to the most likely evolutionary path between them. This analysis has been applied, for example, to drosophila [8, 21], plants =-=[4, 18]-=-, viruses [12], and mammals [7, 20]. Kececloglu and Sankoff [16] gave 2-approximation algorithms on reversal distance, which Bafna and Pevzner [3] improved to a factor of 7/4 approximation. Most recen... |

44 |
Computational complexity and the classification of finite simple groups.
- Babai, Kantor, et al.
- 1983
(Show Context)
Citation Context ...nce of generators for arbitrary permutation groups is PSPACE-complete, even when there are only two generators. The general problem has seen considerable attention -- see the survey of Babai, et. al. =-=[2]-=-. The outline of this paper is as follows. In Section 2 we present our notation for describing sequences of reversal operations. In Section 3, we present our notion of equivalent transformations, whic... |

44 |
Ecient bounds for oriented chromosome inversion distance
- Kececioglu, Sanko
- 1994
(Show Context)
Citation Context ...enhalli and Pevzner [11] gave a polynomial-time algorithm for signed reversal distance, although the problem for unsigned reversals (as we consider in this paper) remains open. Kececloglu and Sankoff =-=[17]-=- report on the success of heuristics and search in determining reversal distance for chromosomes. Bafna and Pevzner [5] present approximation algorithms for transposition distance, ie. under block mov... |

38 |
The complexity of finding minimum length generator sequences.
- Jerrum
- 1985
(Show Context)
Citation Context ... each reversal simply transposes adjacent elements. Bubble sort [19] sorts any permutation �� using exactly one transposition for each inversion in ��, thus minimizing the number of reversals.=-= Jerrum [15]-=- presented a polynomial algorithm for the much more difficult problem of sorting circular permutations using a minimum number of transpositions. Gates and Papadimitriou [9] (also [10]) studied the pro... |

31 |
Inversions in the chromosomes of Drosophila pseudoobscura
- Dobzhansky, Sturtevant
- 1938
(Show Context)
Citation Context ...interval of genes. A shortest reversal sequence sorting one genome to another corresponds to the most likely evolutionary path between them. This analysis has been applied, for example, to drosophila =-=[8, 21]-=-, plants [4, 18], viruses [12], and mammals [7, 20]. Kececloglu and Sankoff [16] gave 2-approximation algorithms on reversal distance, which Bafna and Pevzner [3] improved to a factor of 7/4 approxima... |

26 |
Inversions in the third chromosome of wild races of drosophila pseudoobscura, and their use in the study of the history of the species
- Sturtevant, Dobzhansky
- 1936
(Show Context)
Citation Context ...interval of genes. A shortest reversal sequence sorting one genome to another corresponds to the most likely evolutionary path between them. This analysis has been applied, for example, to drosophila =-=[8, 21]-=-, plants [4, 18], viruses [12], and mammals [7, 20]. Kececloglu and Sankoff [16] gave 2-approximation algorithms on reversal distance, which Bafna and Pevzner [3] improved to a factor of 7/4 approxima... |

17 |
Sorting by insertion of leading element
- Aigner, West
- 1987
(Show Context)
Citation Context ... in determining reversal distance for chromosomes. Bafna and Pevzner [6] present approximation algorithms for transposition distance, ie. under block moves instead of reversals. Related work includes =-=[1]-=-. All of these problems are special cases of determining the diameter of permutation groups. Jerrum [16] showed that the problem of computing the shortest set of generators for arbitrary permutation g... |

12 |
Chloroplast genome rearrangements and the evolution of giant lobelias from herbaceous ancestors
- Knox, Downie, et al.
- 1993
(Show Context)
Citation Context ...s. A shortest reversal sequence sorting one genome to another corresponds to the most likely evolutionary path between them. This analysis has been applied, for example, to drosophila [8, 21], plants =-=[4, 18]-=-, viruses [12], and mammals [7, 20]. Kececloglu and Sankoff [16] gave 2-approximation algorithms on reversal distance, which Bafna and Pevzner [3] improved to a factor of 7/4 approximation. Most recen... |

9 |
Improved bounds for sorting pancakes under a conjecture, manuscript
- Cohen, Blum
- 1993
(Show Context)
Citation Context ...sals. Heydari and Sudborough [13, 14] have tightened these bounds and proved the problem of computing the exact prefix-reversal distance between two permutations is NP-complete. Related work includes =-=[1, 6]-=-. Computing the exact reversal distance of a permutation is of considerable importance in reconstructing the evolutionary history of the genome. Reversal mutations occur often in chromosomes, where ea... |

9 |
Scenarios for genome rearrangements: Herpesvirus evolution as a test case
- Hannenhalli, Chappey, et al.
- 1994
(Show Context)
Citation Context ...ersal sequence sorting one genome to another corresponds to the most likely evolutionary path between them. This analysis has been applied, for example, to drosophila [8, 21], plants [4, 18], viruses =-=[12]-=-, and mammals [7, 20]. Kececloglu and Sankoff [16] gave 2-approximation algorithms on reversal distance, which Bafna and Pevzner [3] improved to a factor of 7/4 approximation. Most recently, Hannenhal... |

9 |
On Sorting by Prefix Reversals and the Diameter of Pancake Networks, Parallel Architectures and Their Efficient Use, in:LNCS 678,
- Heydari, Sudborough
- 1993
(Show Context)
Citation Context ... 11794-4400 ftichen,skienag@cs.sunysb.edu March 25, 1996 1 Introduction Due to applications in reconstructing the evolutionary history of the genome [22] and to the design of interconnection networks =-=[14]-=-, there has been considerable recent interest in problems of sorting permutations with reversals. In this paper, we study the problem of sorting permutations and circular permutations using as few fix... |

6 |
Reversing trains: A turn of the century sorting problem
- Amato, Blum, et al.
- 1989
(Show Context)
Citation Context ...sals. Heydari and Sudborough [13, 14] have tightened these bounds and proved the problem of computing the exact prefix-reversal distance between two permutations is NP-complete. Related work includes =-=[1, 6]-=-. Computing the exact reversal distance of a permutation is of considerable importance in reconstructing the evolutionary history of the genome. Reversal mutations occur often in chromosomes, where ea... |

6 |
Stack of pancakes
- Györi, Turán
- 1978
(Show Context)
Citation Context ...eversals. Jerrum [15] presented a polynomial algorithm for the much more difficult problem of sorting circular permutations using a minimum number of transpositions. Gates and Papadimitriou [9] (also =-=[10]-=-) studied the problem of sorting permutations using prefix reversals (better known as the pancake-flipping problem), where reversals may be of arbitrary length but each must start from the first eleme... |

4 |
X-linked genetic homologies between mouse and
- Davisson
- 1987
(Show Context)
Citation Context ...ting one genome to another corresponds to the most likely evolutionary path between them. This analysis has been applied, for example, to drosophila [8, 21], plants [4, 18], viruses [12], and mammals =-=[7, 20]-=-. Kececloglu and Sankoff [16] gave 2-approximation algorithms on reversal distance, which Bafna and Pevzner [3] improved to a factor of 7/4 approximation. Most recently, Hannenhalli and Pevzner [11] g... |

2 |
The Pancake Problem
- Heydari
- 1993
(Show Context)
Citation Context ...m the first element of permutation. They showed that 5n=3 + 5=3 prefixreversals suffice to sort any permutation, and there are permutations requiring at least 17n=16 reversals. Heydari and Sudborough =-=[13, 14]-=- have tightened these bounds and proved the problem of computing the exact prefix-reversal distance between two permutations is NP-complete. Related work includes [1, 6]. Computing the exact reversal ... |