Computing the Fr\'echet distance between two polygonal curves takes roughly
quadratic time. In this paper, we show that for a special class of curves the
Fr\'echet distance computations become easier. Let P and Q be two polygonal
curves in Rd with n and m vertices, respectively. We prove four
results for the case when all edges of both curves are long compared to the
Fr\'echet distance between them: (1) a linear-time algorithm for deciding the
Fr\'echet distance between two curves, (2) an algorithm that computes the
Fr\'echet distance in O((n+m)log(n+m)) time, (3) a linear-time
d-approximation algorithm, and (4) a data structure that supports
O(mlog2n)-time decision queries, where m is the number of vertices of
the query curve and n the number of vertices of the preprocessed curve