A Faster Algorithm for Maximum Independent Set on Interval Filament Graphs

TL;DR

This paper introduces more efficient algorithms for finding maximum weight independent sets and induced matchings in interval filament graphs, reducing computational complexity from previous methods.

Contribution

It presents the first $O(N^2)$ algorithm for maximum weight independent set and an $O(N^4)$ algorithm for maximum weight induced matching in interval filament graphs, improving prior complexities.

Findings

Maximum weight independent set algorithm runs in $O(N^2)$ time.

Maximum weight induced matching algorithm runs in $O(N^4)$ time.

Significant complexity improvements over previous algorithms.

Abstract

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.