Abstract
A fragmentary pattern is a multiset of non-empty strings, and it matches a string w if all the strings in it occur within w without any overlaps. We study some fundamental issues on computational complexity related to the matching of fragmentary patterns. We show that the fragmentary pattern matching problem is NP-complete, and the problem to find a fragmentary pattern common to two strings that maximizes the pattern score is NP-hard. Moreover, we propose a polynomialtime approximation algorithm for the fragmentary pattern matching, and show that it achieves a constant worst-case approximation ratio if either the strings in a pattern have the same length, or the importance weights of strings in a pattern are proportional to their lengths.
This research is partially supported by Grants-in-Aid for Encouragement of Young Scientists, Japan Society for the Promotion of Science, No. 12780286.
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Hori, H., Shimozono, S., Takeda, M., Shinohara, A. (2001). Fragmentary Pattern Matching: Complexity, Algorithms and Applications for Analyzing Classic Literary Works. In: Eades, P., Takaoka, T. (eds) Algorithms and Computation. ISAAC 2001. Lecture Notes in Computer Science, vol 2223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45678-3_61
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DOI: https://doi.org/10.1007/3-540-45678-3_61
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