Abstract
The paper deals with all pairs approximate parameterized string matching problem with error threshold k, among two sets of equal length strings. Let \(P=\{p_1, ~ p_2, \ldots , p_{n_P}\} \subseteq \varSigma _P^m\) and \(T=\{t_1, ~ t_2, \ldots , t_{n_T}\}\) \(\subseteq \varSigma _T^m\) be two sets of strings where \(|\varSigma _P|=|\varSigma _T|\). For each \(p_i \in P\), the problem is to find \(t_j \in T\) which is approximately parameterized closest to \(p_i\) under the threshold. The solution has complexity \(O(n_P \, n_T \, m)\). We introduce Parikh vector filtering technique in order to preprocess the given strings and avoid the unwanted paired comparisons. The PV-filtering does not change the asymptotic time complexity but rapidly improves running time for small error threshold as shown by experiments.
A preliminary version of this work is submitted as a technical report in Department of Theoretical Computer Science, Faculty of Information Technology, Czech Technical University in Prague [11]. Shibsankar Das was supported by the fellowship of HERITAGE Erasmus Mundus Partnership project for Ph.D. exchange mobility.
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Notes
- 1.
These definitions can also be extended with respect to other error models.
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The author is grateful to Dr. Jan Holub for his helpful comments and suggestions.
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Das, S. (2018). A Filtering Technique for All Pairs Approximate Parameterized String Matching. In: Ghosh, D., Giri, D., Mohapatra, R., Savas, E., Sakurai, K., Singh, L. (eds) Mathematics and Computing. ICMC 2018. Communications in Computer and Information Science, vol 834. Springer, Singapore. https://doi.org/10.1007/978-981-13-0023-3_10
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