A Filtering Technique for All Pairs Approximate Parameterized String Matching

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.