  Simplifying polygonal curves at different levels of detail is an important
problem with many applications. Existing geometric optimization algorithms are
only capable of minimizing the complexity of a simplified curve for a single
level of detail. We present an $O(n^3m)$-time algorithm that takes a polygonal
curve of n vertices and produces a set of consistent simplifications for m
scales while minimizing the cumulative simplification complexity. This
algorithm is compatible with distance measures such as the Hausdorff, the
Fr\'echet and area-based distances, and enables simplification for continuous
scaling in $O(n^5)$ time. To speed up this algorithm in practice, we present
new techniques for constructing and representing so-called shortcut graphs.
Experimental evaluation of these techniques on trajectory data reveals a
significant improvement of using shortcut graphs for progressive and
non-progressive curve simplification, both in terms of running time and memory
usage.
