Partial Curve Matching under the Fréchet Distance∗

Curve matching is a fundamental problem which occurs in many applications. In this paper, we extend the Fréchet distance to measure partial curve similarity, study its properties, and develop efficient algorithms to compute it. In particular, under the L1 or L∞ metrics, we present an algorithm to compute, in O(m2) time, the partial Fréchet distance between a segment and a polygonal curve of size m. We then develop an approximation algorithm that, in O((n+m)3/ε2) time, computes a (1− ε)approximation to the optimal partial Fréchet distance between two polygonal curves of size n and m, respectively. Finally, we propose a third algorithm that, in near quadratic time, computes a (constant) double-sided error approximation to the optimal partial Fréchet distance.