  We provide an algorithm requiring only $O(N^2)$ time to compute the maximum
weight independent set of interval filament graphs. This also implies an
$O(N^4)$ algorithm to compute the maximum weight induced matching of interval
filament graphs. Both algorithms significantly improve upon the previous best
complexities for these problems. Previously, the maximum weight independent set
and maximum weight induced matching problems required $O(N^3)$ and $O(N^6)$
time respectively.
