## Reconstructing a History of Recombinations From a Set of Sequences (1998)

Venue: | Discrete Appl. Math |

Citations: | 40 - 6 self |

### BibTeX

@INPROCEEDINGS{Kececioglu98reconstructinga,

author = {John Kececioglu and Dan Gusfield},

title = {Reconstructing a History of Recombinations From a Set of Sequences},

booktitle = {Discrete Appl. Math},

year = {1998},

pages = {239--260}

}

### Years of Citing Articles

### OpenURL

### Abstract

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 higher-order 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 non-tree-like event that produces a child sequence by crossing two parent sequences. We present polynomial-time 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 NP-complete. Keywords Computational bio...

### Citations

11431 | Computers and Intractability, A Guide to the Theory of NPCompleteness - Garey, Johnson - 1979 |

289 | Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
- Hannenhalli, Pevzner
- 1999
(Show Context)
Citation Context ...constructing an evolutionary history when recombination has occurred. This follows a trend in computational biology to design algorithms that take into account macro-mutations at the chromosome level =-=[25, 5, 6, 24, 13, 14]-=-, in contrast to micro-mutations at the gene level, now that data for whole genomes is becoming available. We introduce two new problems. The first, Recombination Cost, is a generalization of sequence... |

289 |
A linear space algorithm for computing maximal common subsequences
- Hirschberg
- 1975
(Show Context)
Citation Context ... between 1 and 10, so the bounds of Theorem 5 are essentially quadratic time and linear space to determine the minimum number of crossovers. By applying the divide and conquer technique of Hirschberg =-=[17]-=-, one can obtain the corresponding alignment, as well as the minimum number of crossovers, within the same time and space. 3.2 Recombination with point mutation When point mutations are allowed, we do... |

186 |
Statistical properties of the number of recombination events in the history of a sample of DNA sequences
- Hudson, Kaplan
- 1985
(Show Context)
Citation Context ...ossover recombination. In the worst case, m = O(k 3 ), but m may be much smaller. 1.2 Related work Prior work on recombination has largely focused on statistical tests for population genetics studies =-=[18, 19, 22, 36, 40]-=-. Hein [15, 16] appears to be the first to consider the problem from the view of designing an algorithm to reconstruct a history. He presents a heuristic for a Steiner version of the problem in which ... |

169 | Efficient probabilistically checkable proofs and applications to approximation
- Bellare, Goldwasser, et al.
- 1993
(Show Context)
Citation Context ...hose size is at most a constant factor larger than the minimum, for an arbitrary recombination hypergraph, would give a constant-factor approximation for Set Cover. Recent non-approximability results =-=[29, 7]-=- show that such an algorithm would imply P = NP. However, while the minimization problem of approximating the size of the smallest protoset to within a constant factor appears difficult, the maximizat... |

164 |
Genome rearrangements and sorting by reversals
- Bafna, Pevzner
- 1996
(Show Context)
Citation Context ...constructing an evolutionary history when recombination has occurred. This follows a trend in computational biology to design algorithms that take into account macro-mutations at the chromosome level =-=[25, 5, 6, 24, 13, 14]-=-, in contrast to micro-mutations at the gene level, now that data for whole genomes is becoming available. We introduce two new problems. The first, Recombination Cost, is a generalization of sequence... |

130 |
Efficient algorithms for inferring evolutionary trees
- Gusfield
- 1991
(Show Context)
Citation Context ...FG0390ER60999, and National Science Foundation Grant CCR-9103937. Kececioglu and Gusfield 2 segregation, and a number of efficient algorithms for finding such trees have been designed in recent years =-=[1, 8, 12, 20, 45]-=-. However, the two assumptions inherent in a tree model---that the organisms descended from a common ancestor and that descendants arose by segregation---are not always well met by the data. In fact, ... |

116 | Sorting by transpositions
- Bafna, Pevzner
- 1998
(Show Context)
Citation Context ...constructing an evolutionary history when recombination has occurred. This follows a trend in computational biology to design algorithms that take into account macro-mutations at the chromosome level =-=[25, 5, 6, 24, 13, 14]-=-, in contrast to micro-mutations at the gene level, now that data for whole genomes is becoming available. We introduce two new problems. The first, Recombination Cost, is a generalization of sequence... |

98 |
Reconstructing evolution of sequences subject to recombination using parsimony
- Hein
- 1990
(Show Context)
Citation Context ...he worst case, m = O(k 3 ), but m may be much smaller. 1.2 Related work Prior work on recombination has largely focused on statistical tests for population genetics studies [18, 19, 22, 36, 40]. Hein =-=[15, 16]-=- appears to be the first to consider the problem from the view of designing an algorithm to reconstruct a history. He presents a heuristic for a Steiner version of the problem in which the sequence da... |

98 | A heuristic method to reconstruct the history of sequences subject to recombination
- Hein
- 1993
(Show Context)
Citation Context ...he worst case, m = O(k 3 ), but m may be much smaller. 1.2 Related work Prior work on recombination has largely focused on statistical tests for population genetics studies [18, 19, 22, 36, 40]. Hein =-=[15, 16]-=- appears to be the first to consider the problem from the view of designing an algorithm to reconstruct a history. He presents a heuristic for a Steiner version of the problem in which the sequence da... |

87 | Transforming men into mice (polynomial algorithm for genetic distance problem
- Hannenhalli, Pevzner
- 1995
(Show Context)
Citation Context |

81 | A robust model for finding optimal evolutionary tree
- Farach-Colton, Kannan, et al.
- 1993
(Show Context)
Citation Context ...FG0390ER60999, and National Science Foundation Grant CCR-9103937. Kececioglu and Gusfield 2 segregation, and a number of efficient algorithms for finding such trees have been designed in recent years =-=[1, 8, 12, 20, 45]-=-. However, the two assumptions inherent in a tree model---that the organisms descended from a common ancestor and that descendants arose by segregation---are not always well met by the data. In fact, ... |

80 | Exact and approximation algorithms for sorting by reversals, with application to genome rearrangement
- Kececioglu, Sankoff
- 1995
(Show Context)
Citation Context |

72 | An algorithm for approximate tandem repeats
- Landau, Schmidt
- 1993
(Show Context)
Citation Context ...of the parents. This mechanism of crossover leads to many of the more complex events considered by sequence comparison algorithms, including block insertions and deletions [33, 10] and tandem repeats =-=[21, 26]-=-. Recombination, in organisms with pairs of chromosomes, often occurs during meiosis, the stage at which a reproductive cell receives a representative from each chromosome pair. Crossover between the ... |

52 | A Polynomial-Time Algorithm for the Perfect Phylogeny Problem when the Number of Character States is Fixed
- Agarwala, Fernandez-Baca
- 1994
(Show Context)
Citation Context ...FG0390ER60999, and National Science Foundation Grant CCR-9103937. Kececioglu and Gusfield 2 segregation, and a number of efficient algorithms for finding such trees have been designed in recent years =-=[1, 8, 12, 20, 45]-=-. However, the two assumptions inherent in a tree model---that the organisms descended from a common ancestor and that descendants arose by segregation---are not always well met by the data. In fact, ... |

49 |
Speeding up dynamic programming with applications to molecular biology
- Galil, Giancarlo
- 1989
(Show Context)
Citation Context ...hen at the right end of one of the parents. This mechanism of crossover leads to many of the more complex events considered by sequence comparison algorithms, including block insertions and deletions =-=[33, 10]-=- and tandem repeats [21, 26]. Recombination, in organisms with pairs of chromosomes, often occurs during meiosis, the stage at which a reproductive cell receives a representative from each chromosome ... |

33 |
Minimal representation of directed hypergraphs
- Ausiello, Dâ€™Atri, et al.
- 1986
(Show Context)
Citation Context ...eprocessing phase, which analyzes the sequence data, followed by a search phase, which tests candidate protopairs. For multiple-crossover recombination, the search proceeds over a directed hypergraph =-=[3]-=- containing sequence triples. (Each triple represents a directed hyperedge. The first two elements of a triple are the parents in a recombination, and are unordered; the third element of a triple is t... |

31 |
Inferring evolutionary history from DNA sequences
- Kannan, Warnow
- 1994
(Show Context)
Citation Context |

28 | An Algorithm For Locating Non-Overlapping Regions of Maximum Alignment Score
- Kannan, Myers
- 1996
(Show Context)
Citation Context ...of the parents. This mechanism of crossover leads to many of the more complex events considered by sequence comparison algorithms, including block insertions and deletions [33, 10] and tandem repeats =-=[21, 26]-=-. Recombination, in organisms with pairs of chromosomes, often occurs during meiosis, the stage at which a reproductive cell receives a representative from each chromosome pair. Crossover between the ... |

24 | Of Mice and Men: Algorithms for evolutionary distances between genomes with translocation
- Kececioglu, Ravi
- 1995
(Show Context)
Citation Context |

18 |
Dynamic maintenance of directed hypergraphs
- Ausiello, Nanni
- 1990
(Show Context)
Citation Context ...pair individually? It appears not. Testing all pairs is essentially computing the transitive closure of a directed hypergraph, and the bound of Theorem 4 matches the best known bound for that problem =-=[3, 4]-=-. We also note that with a simple modification the algorithm can find a protopair of minimum bottleneck cost. We can maintain list Reachable as a heap, where vertices are prioritized by the weight of ... |

15 |
The use of sample genealogies for studying a selectively neutral m-loci model with recombination. Theoretical Population Biology
- Kaplan, Hudson
- 1985
(Show Context)
Citation Context ...ossover recombination. In the worst case, m = O(k 3 ), but m may be much smaller. 1.2 Related work Prior work on recombination has largely focused on statistical tests for population genetics studies =-=[18, 19, 22, 36, 40]-=-. Hein [15, 16] appears to be the first to consider the problem from the view of designing an algorithm to reconstruct a history. He presents a heuristic for a Steiner version of the problem in which ... |

5 |
Endre Tarjan, "Fibonacci Heap and Their Uses in Improved Network Optimization Algorithms
- Fredman, E
- 1987
(Show Context)
Citation Context ...of minimum bottleneck cost. We can maintain list Reachable as a heap, where vertices are prioritized by the weight of the least-cost in-edge that touches them from set Reached. Using a Fibonacci heap =-=[9]-=-, removing a vertex of minimum priority takes O(log k) time, while updating the priority of a vertex when examining an out-edge takes O(1) time. This adds O(k log k) time to the test for a candidate p... |

2 |
Properties of a neutral model with intragenic recombination
- Hudson
- 1983
(Show Context)
Citation Context ...ossover recombination. In the worst case, m = O(k 3 ), but m may be much smaller. 1.2 Related work Prior work on recombination has largely focused on statistical tests for population genetics studies =-=[18, 19, 22, 36, 40]-=-. Hein [15, 16] appears to be the first to consider the problem from the view of designing an algorithm to reconstruct a history. He presents a heuristic for a Steiner version of the problem in which ... |

1 |
The myriad virtues of subword trees." Combinatorial Algorithms on
- Apostolico
- 1985
(Show Context)
Citation Context ...elf. 3 We can compute PrefLen and SufLen for all pairs of sequences in O(n + k 2 ) time, by building a suffix tree for the sequences and looking up nearest common ancestors in constant time per query =-=[2, 37]-=-. Finding the next reachable sequence, by testing the above inequality on O(k) sequences, takes O(k) time. Adding this sequence to the reached set and updating MaxPrefLen and MaxSufLen also takes O(k)... |