There are several studied similarity measures; among them, Fréchet distance is an essential measure. Consider a man and his dog connected by a leash and walking on two curves at any speed. The Fréchet distance is the minimum leash length needed for walking along the curves.
In this thesis, we work with the discrete version of Fréchet distance where curves are not continuous; instead of the man and the dog walking continuously, they jump over vertices of discrete curves. If we can implement some transformation on curves, we might be able to improve the comparison of curves.
In this thesis, we study the following problem: Given a set of curves $\mathcal{C}$ and a query curve $Q$, if there is a curve with discrete Fréchet distance $r$ (under \emph{translation} or \emph{rotation}) from the queue in set $\mathcal{C}$, we will return a curve $C^{\star}$ with distance $(1 + \epsilon)r$ from $Q$.