Given two sets of points, the text and the pattern, determining whether the pattern "appears" in the text is modeled as the point set pattern matching problem. Applications usually ask for not only exact matches between these two sets, but also approximate matches. In this paper, we investigate a one-dimensional approximate point set matching problem proposed in [T. Suga and S. Shimozono, Approximate point set pattern matching on sequences and planes, CPM'04]. What requested is an optimal match which minimizes the L p -norm of the difference vector (|p2 - p1 - (t′2 - t′1)|, |p3 - p2 - (t′3 - t′2)|,..., |p m - p m - 1 - (t′m - t′m - 1)|), where p1, p2,..., pm is the pattern and t′1, t′2,..., t′m is a subsequence of the text. For p → ∞, the proposed algorithm is of time complexity O(mn), where m and n denote the lengths of the pattern and the text, respectively. For arbitrary p < ∞, the time complexity is O(mnT(p)), where T(p) is the time of evaluating xp for x ∈ R. © 2011 Springer-Verlag.
CITATION STYLE
Wang, H. L., & Chen, K. Y. (2011). Approximate point set pattern matching with Lp-norm. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7024 LNCS, pp. 81–86). https://doi.org/10.1007/978-3-642-24583-1_9
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