## A Scalable and Efficient Systolic Algorithm for the Longest Common Subsequence Problem (2002)

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Venue: | Journal of Information Science and Engineering |

Citations: | 1 - 0 self |

### BibTeX

@ARTICLE{Lin02ascalable,

author = {Yen-chun Lin and Jih-wei Yeh},

title = {A Scalable and Efficient Systolic Algorithm for the Longest Common Subsequence Problem},

journal = {Journal of Information Science and Engineering},

year = {2002},

volume = {18},

pages = {519--532}

}

### OpenURL

### Abstract

this paper, a scalable and efficient systolic algorithm is presented. For two given strings of length m and n,wherem # n,the algorithm can solve the LCS problem in m +2r -- 1 (respectively n +2r -- 1) time steps with r < n/2 (respectively r < m/2) processors. Experimental results show that the algorithm can be faster on multicomputers than all the previous systolic algorithms for the same problem

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Citation Context ...B(2)…B(j) to make the context meaningful. In addition, let L(i, 0)=L(0, j) =L(0, 0) =0andLCS(i, 0)=LCS(0, j) =LCS(0, 0) = ε, where ε denotes the empty string. By combining two properties presented=-= in [7, 12], we have the following -=-property: Property 1. For 1 ≤ i ≤ m and 1 ≤ j ≤ n, if A(i)=B(j)then L(i, j)=L(i –1,j –1)+1 LCS(i, j)=LCS(i –1,j –1)B(j) else if L(i, j –1)≥ L(i –1,j)then L(i, j)=L(i, j –1) LCS... |

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Citation Context ...log n) time [17]. Because it is infeasible to build a PRAM with more than a few tens of PEs, the PRAM models are not practical for this problem when m and n are large. In contrast, the systolic model =-=[10]-=- is practical for the LCS problem. A systolic architecture is a regular array of identical PEs. It can be implemented with VLSI chips or a distributed-memory multicomputer that has many more PEs than ... |

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Citation Context ...on, Dec. 6-8, 2000, Chiayi, Taiwan. 519s520 YEN-CHUN LIN AND JIH-WEI YEH The sequential time complexity of the LCS problem has been shown to be Ω (mn) when the number of distinct symbols is not fixe=-=d [2]-=-. Sequential algorithms achieving this time bound can be found in [3, 7-9, 20, 26]. Since m and n are usually very large for typical applications, parallel algorithms for solving the LCS problem are d... |

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Citation Context ...y to achieve high performance. Many systolic algorithms for the LCS problem have been proposed. Robert and Tchuente proposed using a 2-D systolic array to solve the LCS problem in m +5n –3 time step=-=s [22, 23]. Li-=-n uses a linear systolic array of n PEs to solve the problem in m + 4n – 2 time steps [13]. Luce and Myoupo solved the problem on a linear array of n PEs in m +3n + p – 1 time steps [18]. Lecroq e... |

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Citation Context ...y to achieve high performance. Many systolic algorithms for the LCS problem have been proposed. Robert and Tchuente proposed using a 2-D systolic array to solve the LCS problem in m +5n –3 time step=-=s [22, 23]. Li-=-n uses a linear systolic array of n PEs to solve the problem in m + 4n – 2 time steps [13]. Luce and Myoupo solved the problem on a linear array of n PEs in m +3n + p – 1 time steps [18]. Lecroq e... |

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Citation Context ...el, or coalescing, method and the locally parallel globally sequential, or cut-and-pile, technique may be applied to obtain a new systolic algorithm using fewer PEs to solve the same problem instance =-=[11, 21]-=-. In this paper, we use a very different method to obtain a scalable and efficient systolic algorithm that can cope with any LCS problem instances on a linear array of any number of PEs, providing the... |

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Citation Context ...bert and Tchuente proposed using a 2-D systolic array to solve the LCS problem in m +5n –3 time steps [22, 23]. Lin uses a linear systolic array of n PEs to solve the problem in m + 4n – 2 time st=-=eps [13]. -=-Luce and Myoupo solved the problem on a linear array of n PEs in m +3n + p – 1 time steps [18]. Lecroq et al. proposed using a linear array of n PEs to solve the problem in m +2n time steps [12]. Li... |

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Citation Context ...PEs and takes m +2⎡n/2⎤ – 1 time steps [16], in which two symbols of string B are input at a time. It should be noted that no automatic approaches have been used to synthesize LCS systolic algor=-=ithms [19]-=-. All the above-mentioned systolic algorithms require a fixed number of PEs when m and n are known. If the number available of PEs cannot meet the requirement, the systolic algorithms should be modifi... |

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Citation Context ...he exact lower bound on the number of time steps when m + n symbols are input sequentially [14, 15]. Lin and Yeh introduced a systolic algorithm that uses ⎡n/2⎤ PEs and takes m +2⎡n/2⎤ – 1 t=-=ime steps [16]-=-, in which two symbols of string B are input at a time. It should be noted that no automatic approaches have been used to synthesize LCS systolic algorithms [19]. All the above-mentioned systolic algo... |

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Citation Context ...steps [22, 23]. Lin uses a linear systolic array of n PEs to solve the problem in m + 4n – 2 time steps [13]. Luce and Myoupo solved the problem on a linear array of n PEs in m +3n + p – 1 time st=-=eps [18]-=-. Lecroq et al. proposed using a linear array of n PEs to solve the problem in m +2n time steps [12]. Lin and Chen devised two systolic algorithms that use a linear array of n PEs to solve the problem... |