## Divide-and-conquer frontier search applied to optimal sequence alignment (2000)

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Venue: | In National Conference on Artificial Intelligence (AAAI |

Citations: | 48 - 5 self |

### BibTeX

@INPROCEEDINGS{Korf00divide-and-conquerfrontier,

author = {Richard E. Korf},

title = {Divide-and-conquer frontier search applied to optimal sequence alignment},

booktitle = {In National Conference on Artificial Intelligence (AAAI},

year = {2000},

pages = {910--916}

}

### Years of Citing Articles

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### Abstract

We present a new algorithm that reduces the space complexity of heuristic search. It is most e ective for problem spaces that grow polynomially with problem size, but contain large numbers of short cycles. For example, the problem of nding an optimal global alignment ofseveral DNA or amino-acid sequences can be solved by nding a lowest-cost corner-to-corner path in a d-dimensional grid. A previous algorithm, called divide-and-conquer bidirectional search (Korf 1999), saves memory by storing only the Open lists and not the Closed lists. We show that this idea can be applied in a unidirectional search aswell. This extends the technique to problems where bidirectional search is not applicable, and is more e cient in both time and space than the bidirectional version. If n is the length of the strings, and d is the number of strings, this algorithm can reduce the memory requirement from O(n d) to O(n d;1). While our current implementation of DCFS is somewhat slower than existing dynamic programming approaches for optimal alignment of multiple gene sequences, DCFS is a more general algorithm 1

### Citations

1554 | A note on two problems in connexion with graphs
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- 1959
(Show Context)
Citation Context ... consider here algorithms that are guaranteed to find optimal alignments. Problems that Fit in Memory If the grid is small enough to fit into memory, Dijkstra’s single-source shortest path algorithm (=-=Dijkstra, 1959-=-) will solve the problem in time and space, for two strings of length . The particular problem of sequence alignment, as opposed to the general shortest-path problem, can also be solved by a much simp... |

1486 |
A general method applicable to the search for similarities in the amino acid sequences of two proteins
- Needleman, Wunsch
- 1970
(Show Context)
Citation Context ...different genes, and identifying subsequences that are conserved between them. This problem can be mapped to the problem of finding a lowest-cost path from corner to corner in a two-dimensional grid (=-=Needleman and Wunsch, 1970-=-). One sequence is placed on the horizontal axis from left to right, and the other sequence on the vertical axis, from top to bottom. An alignment is represented by a path from the upper-left corner o... |

1037 |
A formal basis for the heuristic determination of minimum cost paths
- Hart, Nilsson, et al.
- 1968
(Show Context)
Citation Context ...10,000 each, or three strings of length 464 each. Problems that Don’t Fit in Memory The interesting case is when the grid doesn’t fit in memory. One approach is to use a heuristic search, such as A* (=-=Hart, Nilsson, and Raphael, 1968-=-), to reduce the size of the search. This requires efficiently computing a lower bound on the cost of a given alignment, and has been applied to sequence alignment by (Ikeda and Imai, 1999). Unfortuna... |

426 | Depth-first iterative-deepening: An optimal admissible tree search
- Korf
- 1985
(Show Context)
Citation Context ...tes, and is still memory limited. The memory limitation of best-first search algorithms like Dijkstra’s and A* has been addressed (Korf, 1995). Many algorithms, such as iterative-deepening-A* (IDA*) (=-=Korf, 1985-=-), rely on depth-first search to avoid this memory limitation. The key idea is that a depth-first search only has to store the path of nodes from the start to the current node, and hence only requires... |

279 |
A linear space algorithm for computing maximal common subsequences
- Hirschberg
- 1975
(Show Context)
Citation Context ...e 1: Sequence alignment as path-finding in a grid the pair of strings that contain them. Overview We first discuss existing techniques for this problem. These include a dynamic programming algorithm (=-=Hirschberg, 1975-=-), a bounded dynamic programming algorithm (Spouge, 1989), and our previous best-first search algorithm, divide-and-conquer bidirectional search (DCBDS) (Korf, 1999). These methods save memory by only... |

216 |
Introduction to Computational Molecular Biology
- Setubal, Meidanis
- 1997
(Show Context)
Citation Context ...owest-cost path in a cube from one corner to the opposite corner. The cost of a multiple alignment is often computed as the sum-of-pairs cost, or the sum of each of the different pairwise alignments (=-=Setubal and Meidanis, 1997-=-). Equivalently, we can score each character position by summing the cost of each of the character pairs. For example, if we have a C, aG, and a gap at one position, the cost at that position is two g... |

197 | Algorithms for approximate string matching - Ukkonen - 1985 |

63 | Improving the practical space and time efficiency of the shortest-paths approach to sum-of-pairs multiple sequence alignment - Gupta, Kececioglu, et al. - 1995 |

33 | Depth- rst iterative-deepening: An optimal admissible tree search - Korf - 1985 |

32 | Bidirectional heuristic search reconsidered
- Kaindl, Kainz
- 1997
(Show Context)
Citation Context ...c search because it generates fewer nodes, takes less time per node generation, requires less memory, and is easier to implement. For a more thorough treatment of bidirectional heuristic search, see (=-=Kaindl and Kainz, 1997-=-). Experimental Results We tested our algorithms on random sequence alignment problems. Each triple of DNA base pairs encodes one of 20 different amino acids. For each problem instance we generated ra... |

25 |
Divide-and-conquer bidirectional search: First results
- Korf
(Show Context)
Citation Context ...nment of several DNA or amino-acid sequences can be solved by finding a lowest-cost corner-tocorner path in a �-dimensional grid. A previous algorithm, called divide-and-conquer bidirectional search (=-=Korf 1999-=-), saves memory by storing only the Open lists and not the Closed lists. We show that this idea can be applied in a unidirectional search as well. This extends the technique to problems where bidirect... |

17 |
Enhanced A* algorithms for multiple alignments: optimal alignments for several sequences and k-opt approximate alignments for large cases. Theoretical Computer Science (210):341–374
- Ikeda, Imai
- 1999
(Show Context)
Citation Context ...Hart, Nilsson, and Raphael, 1968), to reduce the size of the search. This requires efficiently computing a lower bound on the cost of a given alignment, and has been applied to sequence alignment by (=-=Ikeda and Imai, 1999-=-). Unfortunately, A* stores every node it generates, and is still memory limited. The memory limitation of best-first search algorithms like Dijkstra’s and A* has been addressed (Korf, 1995). Many alg... |

14 | Stochastic node caching for memory-bounded search
- Miura, Ishida
- 1998
(Show Context)
Citation Context ...e numbers further. As a result, depth-first searches are completely hopeless on this problem. Other techniques, such as caching some nodes that are generated, have been applied to sequence alignment (=-=Miura and Ishida, 1998-=-). The difficulty with these techniques is that they can only cache a small fraction of the total nodes generated on a large problem, and can only solve relatively easy problems. Hirschberg’s Algorith... |

12 |
Speeding up dynamic programming algorithms for finding optimal lattice paths
- Spouge
- 1989
(Show Context)
Citation Context ...f strings that contain them. Overview We first discuss existing techniques for this problem. These include a dynamic programming algorithm (Hirschberg, 1975), a bounded dynamic programming algorithm (=-=Spouge, 1989-=-), and our previous best-first search algorithm, divide-and-conquer bidirectional search (DCBDS) (Korf, 1999). These methods save memory by only storing the frontier nodes of the search, and not the i... |

8 |
Space-efficient search algorithms
- Korf
- 1995
(Show Context)
Citation Context ...(Ikeda and Imai, 1999). Unfortunately, A* stores every node it generates, and is still memory limited. The memory limitation of best-first search algorithms like Dijkstra’s and A* has been addressed (=-=Korf, 1995-=-). Many algorithms, such as iterative-deepening-A* (IDA*) (Korf, 1985), rely on depth-first search to avoid this memory limitation. The key idea is that a depth-first search only has to store the path... |

2 | Improving the practical space and time e#- ciency of the shortest-paths approach to sum-of-pairs multiple sequence alignment - Gupta, Kececioglu, et al. - 1995 |

1 | Space-e cient search algorithms - Korf - 1995 |

1 | Speeding up dynamic programming algorithms for nding optimal lattice paths - Spouge - 1989 |