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Bit-parallel approach to approximate string matching in compressed texts

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5 Author(s)
Matsumoto, T. ; Dept. of Inf., Kyushu Univ., Fukuoka, Japan ; Kida, T. ; Takeda, M. ; Shinohara, A.
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Addresses the problem of approximate string matching on compressed text. We consider this problem for a text string described in terms of a collage system, which is a formal system proposed by T. Kida et al. (1999) that captures various dictionary-based compression methods. We present an algorithm that exploits bit-parallelism, assuming that our problem fits in a single machine word, e.g. (m-k)(k+1)⩽L, where m is the pattern length, k is the number of allowed errors and L is the length, in bits, of the machine word. For a class of simple collage systems, the algorithm runs in O(k2(||𝒟||+|𝒮|)+km) time using O(k2||𝒟||) space, where ||𝒟|| is the size of dictionary 𝒟 and |𝒮| is the number of tokens in the sequence 𝒮. The LZ78 (Lempel-Ziv, 1978) and the LZW (Lempel-Ziv-Welch, 1984) compression methods are covered by this class. Since we can regard n=||𝒟||+|𝒮| as the compressed length, the time and space complexities are O(k2n+km) and O(k 2n), respectively. For general k and m, they become O(k3 mn/L+km) and O(k3mn/L). Thus, our algorithm is competitive to the algorithm proposed by J. Kärkkäinen, et al. (2000), which runs in O(km) time using O(kmn) space, when k=O(√L)

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String Processing and Information Retrieval, 2000. SPIRE 2000. Proceedings. Seventh International Symposium on

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