Young Ho Kim , Ju Hui Jeong , Dae Woong Kang , Jeong Seop Sim

KIPS Transactions on Computer and Communication Systems, Vol. 2, No. 2, pp. 67-74, Feb. 2013
10.3745/KTCCS.2013.2.2.67,   PDF Download:

Abstract

Approximate string matching problems have been studied in diverse fields. Recently, fast approximate string matching algorithms are being used to reduce the time and costs for the next generation sequencing. To measure the amounts of errors between two strings, we use a distance function such as the edit distance. Given two strings X(|X|=m) and Y (|Y|=n) over an alphabet ∑, the edit distance betweenX and Y is the minimum number of edit operations to convert X into Y. The edit distance between X and Y can be computed using the well-known dynamic programming technique in O (m n) time and space. The edit distance also can be computed using the Four-Russians` algorithm whose preprocessing step runs in O((3|∑|)²t t²) time and O((3|∑|)²t t) space and the computation step runs in O(m n/t) time andO(m n) space where t represents the size of the block. In this paper, we present a parallelized version of the computation step of the Four-Russians` algorithm. Our algorithm computes the edit distance between X and Y in O (m +n) time using m/t threads. Then we implemented both the sequential version and our parallelized version of the Four-Russians` algorithm using CUDA to compare the execution times. When t=1 and t=2, our algorithm runs about 10 times and 3 times faster than the sequential algorithm, respectively.

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