Covering a Curve with Subtrajectories

We study subtrajectory clustering under the Fr\'echet distance. Given a polygonal curve $P$ with $n$ vertices, and parameters $k$ and $\ell$, the goal is to find $k$ center curves of complexity at most $\ell$ such that every point on $P$ is covered by a subtrajectory that has small Fr\'echet distance to one of the $k$ center curves. We suggest a new approach to solving this problem based on a set cover formulation leading to polynomial-time approximation algorithms. Our solutions rely on carefully designed set system oracles for systems of subtrajectories.