  In the Euclidean TSP with neighborhoods (TSPN), we are given a collection of
$n$ regions (neighborhoods) and we seek a shortest tour that visits each
region. In the path variant, we seek a shortest path that visits each region.
We present several linear-time approximation algorithms with improved ratios
for these problems for two cases of neighborhoods that are (infinite) lines,
and respectively, (half-infinite) rays. Along the way we derive a tight bound
on the minimum perimeter of a rectangle enclosing an open curve of length $L$.
