  We study a trajectory analysis problem we call the Trajectory Capture Problem
(TCP), in which, for a given input set ${\cal T}$ of trajectories in the plane,
and an integer $k\geq 2$, we seek to compute a set of $k$ points (``portals'')
to maximize the total weight of all subtrajectories of ${\cal T}$ between pairs
of portals. This problem naturally arises in trajectory analysis and
summarization.
  We show that the TCP is NP-hard (even in very special cases) and give some
first approximation results. Our main focus is on attacking the TCP with
practical algorithm-engineering approaches, including integer linear
programming (to solve instances to provable optimality) and local search
methods. We study the integrality gap arising from such approaches. We analyze
our methods on different classes of data, including benchmark instances that we
generate. Our goal is to understand the best performing heuristics, based on
both solution time and solution quality. We demonstrate that we are able to
compute provably optimal solutions for real-world instances.
