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.

翻译：我们提供的算法仅需要$O(N)2美元的时间来计算最大重量,以独立计算一组间隙丝形图。这还意味着计算最大重量引引引的间隙丝形图的最大比值的算法$O(N)4)美元。这两种算法都大大改进了以前这些问题的最复杂程度。以前,最大重量独立设定和最大重量引致的匹配问题分别需要$O(N)3美元和$O(N)6美元的时间。