## Going Against The Grain (1996)

Venue: | Proc. 3rd South American Workshop on String Processing, International Informatics Series #4 |

Citations: | 1 - 1 self |

### BibTeX

@INPROCEEDINGS{Myers96goingagainst,

author = {Gene Myers and Mudita Jain},

title = {Going Against The Grain},

booktitle = {Proc. 3rd South American Workshop on String Processing, International Informatics Series #4},

year = {1996},

pages = {203--213}

}

### OpenURL

### Abstract

. We review a general, space and time efficient technique for delivering a sequence of values computable by a recurrence relation, in the order opposing the data-dependencies of the recurrence. The technique provides a series of time/space tradeoffs we characterize by parameter K ? 0. Namely, N values can be delivered against the grain in O(KN) time and O(KN 1=K ) space. This basic idea is not new, but here we present it in a framework exposing its essential nature and we give a concise yet easily understood explanation of it in terms of counting in a radix-N 1=K number system. We then show how to apply this paradigm to a couple of problems in sequence comparison, a domain where it has here to fore not been used. We show that in the limiting case of K = log 2 N , the method coincides with the well-known divideand -conquer algorithm of Hirschberg. Thus, our observation provides a continuum of time/space tradeoffs for all comparison problems that have appealed to the Hirschberg para...

### Citations

81 | A new algorithm for best subsequence alignments with application to tRNA-rRNA comparisons
- Waterman, Eggert
- 1987
(Show Context)
Citation Context ...to the recurrence for either P (i; j) and/or S(i; j). The one potential difficulty of such an approach is that there may be many "interesting" local alignments. In the approach of Waterman a=-=nd Eggert [14]-=-, this problem is resolved by finding the highest scoring path, removing it, finding the next highest path, removing it, and so on. While conceptually simple, this approach does have the disadvantages... |

68 |
Sequence comparison with concave weighting functions
- Miller, Myers
- 1988
(Show Context)
Citation Context ...t of columns in any order desired. Since many sequence comparison results appeal to variations of Hirschberg's divide-and-conquer algorithm to deliver alignment in an efficient amount of space (e.g., =-=[6, 8]-=-), it follows that our central idea is immediately applicable and gives one the flexibility of a series of time/space tradeoffs parameterized by K. Returning to the suboptimal paths problem, we now sh... |

65 |
Approximate matching of regular expression
- Miller, Myers
- 1989
(Show Context)
Citation Context ...t of columns in any order desired. Since many sequence comparison results appeal to variations of Hirschberg's divide-and-conquer algorithm to deliver alignment in an efficient amount of space (e.g., =-=[6, 8]-=-), it follows that our central idea is immediately applicable and gives one the flexibility of a series of time/space tradeoffs parameterized by K. Returning to the suboptimal paths problem, we now sh... |

61 |
Identification of the common molecular sequences
- Smith, Waterman
- 1981
(Show Context)
Citation Context ...sequence that are unusually similar. In terms of the edit graph, this local alignments problem requires finding paths in the graph of unusually high score. In the basic approach of Smith and Waterman =-=[12]-=-, the underlying scoring scheme is assumed to be negatively biased so that the expected value of any path is negative. One then asks for subpaths of maximum (positive) score. This is easily accomplish... |

47 |
Efficient worst-case data structures for range searching
- Bentley, Maurer
- 1980
(Show Context)
Citation Context ... a problem. This paradigm has appeared several times in the context of specific problem domains. For example, we believe it was first used by Bentley and Maurer in "dynamizing" static search=-= problems [1]-=-, later by Myers in realizing persistent arrays [7], and by Kannan and Myers in finding twins [5]. However the paradigm has never been presented as one of going against the grain and has not been appl... |

36 |
Efficient applicative data types
- Myers
- 1984
(Show Context)
Citation Context ...s in the context of specific problem domains. For example, we believe it was first used by Bentley and Maurer in "dynamizing" static search problems [1], later by Myers in realizing persiste=-=nt arrays [7]-=-, and by Kannan and Myers in finding twins [5]. However the paradigm has never been presented as one of going against the grain and has not been applied in a general way to sequence comparison. Moreov... |

31 |
Pattern recognition genetic sequences by mismatch density
- Sellers
- 1984
(Show Context)
Citation Context ...eated recomputation of regions of the dynamic programming matrix and of requiring the space to store all previously reported local alignments. Another unpublished proposal was made by Sellers in 1987 =-=[10, 11]-=- that is interesting and involves only a single pass. Let GP be the graph whose edges give rise to the P -values at each vertex, i.e., v ! w 2 GP iff P (v)+ ffi (v ! w) = P (w). Similarly, let GS be t... |

29 | A dynamic programming algorithm to find all solutions in a neighborhood of the optimum
- Waterman, Byers
- 1985
(Show Context)
Citation Context ...path from (0; 0) to (M; N ) that passes through (i; j). A series of results in the literature concern enumerating all suboptimal paths that score within some threshold �� , typically near the opti=-=mum [13, 9, 2]. Si-=-nce the number of such alignments grows very rapidly as �� moves away from the optimum, investigators have found it superior to depict the subgraph of the edit graph containing the paths represent... |

28 | An Algorithm For Locating Non-Overlapping Regions of Maximum Alignment Score
- Kannan, Myers
- 1996
(Show Context)
Citation Context ...For example, we believe it was first used by Bentley and Maurer in "dynamizing" static search problems [1], later by Myers in realizing persistent arrays [7], and by Kannan and Myers in find=-=ing twins [5]-=-. However the paradigm has never been presented as one of going against the grain and has not been applied in a general way to sequence comparison. Moreover, in the next two paragraphs we concisely an... |

21 |
A linear space algorithm for computing longest common subsequences
- Hirschberg
- 1975
(Show Context)
Citation Context ...requires only O(M log N ) space when K is chosen to be log 2 N . At this juncture we digress to make the observation that our approach generalizes the basic divide and conquer algorithm of Hirschberg =-=[4]-=-. To see this observe that in the case that K = log 2 N , the set of S-vectors cached at any moment is exactly the set of mid-point vectors that would be on the recursion stack of the divide-and-conqu... |

10 | On suboptimal alignments of biological sequences
- Naor, Brutlag
- 1993
(Show Context)
Citation Context ...path from (0; 0) to (M; N ) that passes through (i; j). A series of results in the literature concern enumerating all suboptimal paths that score within some threshold �� , typically near the opti=-=mum [13, 9, 2]. Si-=-nce the number of such alignments grows very rapidly as �� moves away from the optimum, investigators have found it superior to depict the subgraph of the edit graph containing the paths represent... |

8 | Computing all suboptimal alignments in linear space
- Chao
- 1994
(Show Context)
Citation Context ...path from (0; 0) to (M; N ) that passes through (i; j). A series of results in the literature concern enumerating all suboptimal paths that score within some threshold �� , typically near the opti=-=mum [13, 9, 2]. Si-=-nce the number of such alignments grows very rapidly as �� moves away from the optimum, investigators have found it superior to depict the subgraph of the edit graph containing the paths represent... |

5 | Parallel sequence alignment in limited space
- Grice, Hughey, et al.
- 1995
(Show Context)
Citation Context ...in-based algorithm, is that for different choices of K one gets a tradeoff in space and time, thus generalizing the divide-and-conquer approach. Indeed, in a recent independent discovery Grice et al. =-=[3]-=- also arrived at an algorithm like the recursive formulation given in Figure 1. Procedure D and C(start,end: integer, p,s: array [0 \Delta \Delta \Delta M ] of real) f Var P; S: array [0 \Delta \Delta... |

2 |
personal communication
- Sellers
- 1968
(Show Context)
Citation Context ...eated recomputation of regions of the dynamic programming matrix and of requiring the space to store all previously reported local alignments. Another unpublished proposal was made by Sellers in 1987 =-=[10, 11]-=- that is interesting and involves only a single pass. Let GP be the graph whose edges give rise to the P -values at each vertex, i.e., v ! w 2 GP iff P (v)+ ffi (v ! w) = P (w). Similarly, let GS be t... |