One-dimensional approximate point set pattern matching with L p-norm

Hung Lung Wang*, Kuan Yu Chen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 pattern matching problem proposed in [19]. We generalize the measure between approximate matches from L1-norm to Lp-norm. More specifically, what requested is an optimal match which minimizes the Lp-norm of the difference vector (| p2-p1-(t2′-t1′)|,|p3- p2-(t3′-t2′)|,.,|Pm-pm-1- (tm′-tm-1′)|), where p1,p2,.,Pm is the pattern and t1′,t2′,.,tm′ is a subsequence of the text. For p→∞, we propose an O(mn)-time algorithm, where m and n denote the lengths of the pattern and the text, respectively. For arbitrary p<∞, we propose an algorithm which runs in O(mnT(p)) time, where T(p) is the time of evaluating xp for xεR.

Original languageEnglish
Pages (from-to)42-50
Number of pages9
JournalTheoretical Computer Science
Publication statusPublished - 2014 Feb 13
Externally publishedYes


  • Dynamic programming
  • L-norm
  • Point set pattern matching

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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