An Improved Parameterized Algorithm for the Independent Feedback Vertex Set Problem

TL;DR

This paper presents a new parameterized algorithm for the Independent Feedback Vertex Set problem that improves the upper bound from previous algorithms, making it more efficient for larger graphs.

Contribution

The paper introduces an improved parameterized algorithm for the IFVS problem with a better time complexity bound of O(4^k n^2), surpassing previous results.

Findings

Achieved a time complexity of O(4^k n^2) for the IFVS problem.

Improved the upper bound from O*(5^k n^O(1)) to a more efficient algorithm.

Demonstrated the effectiveness of the new algorithm through theoretical analysis.

Abstract

In this paper, we develop a new parameterized algorithm for the {\sc Independent Feedback Vertex Set} (IFVS) problem. Given a graph $G=(V,E)$, the goal of the problem is to determine whether there exists a vertex subset $F\subseteq V$ such that $V-F$ induces a forest in $G$ and $F$ is an independent set. We show that there exists a parameterized algorithm that can determine whether a graph contains an IFVS of size $k$ or not in time $O(4^kn^{2})$. To our best knowledge, this result improves the known upper bound for this problem, which is $O^{*}(5^{k}n^{O(1)})$.