  The congestion of a curve is a measure of how much it zigzags around locally.
More precisely, a curve $\pi$ is $c$-packed if the length of the curve lying
inside any ball is at most $c$ times the radius of the ball, and its congestion
is the maximum $c$ for which $\pi$ is $c$-packed. This paper presents a
randomized $(288+\varepsilon)$-approximation algorithm for computing the
congestion of a curve (or any set of segments in constant dimension). It runs
in $O( n \log^2 n)$ time and succeeds with high probability. Although the
approximation factor is large, the running time improves over the previous
fastest constant approximation algorithm \cite{gsw-appc-20}, which runs in
(roughly) $O(n^{4/3})$ time. We carefully combine new ideas with known
techniques to obtain our new, near-linear time algorithm.
