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Strict approximate pattern matching with general gaps

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Abstract

Pattern matching with gap constraints is one of the essential problems in computer science such as music information retrieval and sequential pattern mining. One of the cases is called loose matching, which only considers the matching position of the last pattern substring in the sequence. One more challenging problem is considering the matching positions of each character in the sequence, called strict pattern matching which is one of the essential tasks of sequential pattern mining with gap constraints. Some strict pattern matching algorithms were designed to handle pattern mining tasks, since strict pattern matching can be used to compute the frequency of some patterns occurring in the given sequence and then the frequent patterns can be derived. In this article, we address a more general strict approximate pattern matching with Hamming distance, named SAP (Strict Approximate Pattern matching with general gaps and length constraints), which means that the gap constraints can be negative. We show that a SAP instance can be transformed into an exponential amount of the exact pattern matching with general gaps instances. Hence, we propose an effective online algorithm, named SETA (SubnETtree for sAp), based on the subnettree structure (a Nettree is an extension of a tree with multi-parents and multi-roots) and show the completeness of the algorithm. The space and time complexities of the algorithm are O(m × Maxlen × W × d) and O(Maxlen × W × m 2 × n × d), respectively, where m, Maxlen, W, and d are the length of pattern P, the maximal length constraint, the maximal gap length of pattern P and the approximate threshold. Extensive experimental results validate the correctness and effectiveness of SETA.

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Acknowledgments

This research is supported by the National Natural Foundation of China under grants No. 61229301 and 61370144, the Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT) of the Ministry of Education, China, under grant IRT13059, the Natural Science Foundation of Hebei Province of China under grant No. F2013202138, and the Key Project of the Educational Commission of Hebei Province under grant No. ZH2012038.

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Authors and Affiliations

  1. School of Computer Science and Engineering, Hebei University of Technology, Tianjin, 300130, China

    Youxi Wu & Shuai Fu

  2. School of Software, Dalian University of Technology, Dalian, 116621, China

    He Jiang

  3. School of Computer Science and Information Engineering, Hefei University of Technology, Hefei, 230009, China

    Xindong Wu

  4. Department of Computer Science, University of Vermont, Burlington, VT, 05405, USA

    Xindong Wu

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  1. Youxi Wu
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  2. Shuai Fu
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  3. He Jiang
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Correspondence to Youxi Wu.

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Wu, Y., Fu, S., Jiang, H. et al. Strict approximate pattern matching with general gaps. Appl Intell 42, 566–580 (2015). https://doi.org/10.1007/s10489-014-0612-3

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  • DOI: https://doi.org/10.1007/s10489-014-0612-3

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