One-dimensional approximate point set pattern matching with Lp L p -norm ?
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 L 1 -norm to Lp L p -norm. More specifically, what requested is an optimal match which minimizes the Lp L p -norm of the difference vector ( | p 2 ? p 1 ? ( t 2 ? ? t 1 ? ) | , | p 3 ? p 2 ? ( t 3 ? ? t 2 ? ) | ,  , | p m ? p m ? 1 ? ( t m ? ? t m ? 1 ? ) | ) , where p1,p2,,pm p 1 , p 2 ,  , p m is the pattern and t 1 ? , t 2 ? ,  , t m ? is a subsequence of the text. For p?? p ? ? , we propose an O(mn) O ( m n ) -time algorithm, where m and n  denote the lengths of the pattern and the text, respectively. For arbitrary p<? p < ? , we propose an algorithm which runs in O(mnT(p)) O ( m n T ( p ) ) time, where T(p) T ( p ) is the time of evaluating xp x p for x?R x ? R .
point set pattern matching lp l p -norm lp l p lp l p l p dynamic programming