Before revision:  A relevant operation on curves is similarity search : given a dataset S of curves , construct a data structure that, for any query curve q, finds the curves in S similar to q. Similarity search is a computational demanding task, in particular when a robust distance function is used, such as the continuous Fr\'echet distance.
After revision:  A relevant operation on curves is similarity search : given a dataset S of n polygonal curves and a threshold r>0 , construct a data structure that, for any query curve q, finds the curves in S similar to q. Similarity search is a computational demanding task, in particular when a robust distance function is used, such as the continuous Fr\'echet distance.