Fix a metric space $(M, d)$. A sequence of points in $M$ is called a curve. Consider two curves $x, y$ of length $n, m (n \geq m)$. We may traverse $x$ and $y$ by starting in their first entries, in any time step advancing to the next entry in $x$ or $y$ or both, and ending in their last entries. The cost of such a traversal is the sum over all points in time of the distance between the current entries. The dynamic time warping distance of $x$ and $y$ is the minimal cost of any traversal.