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In this paper, we develop a new parameterized algorithm for the {\scIndependent Feedback Vertex Set} (IFVS) problem. Given a graph $G=(V,E)$, thegoal 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 anindependent set. We show that there exists a parameterized algorithm that candetermine 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 upperbound for this problem, which is $O^{*}(5^{k}n^{O(1)})$.

An Improved Parameterized Algorithm for the Independent Feedback Vertex Set Problem