  In this work, we study the Induced Matching problem: Given an undirected
graph $G$ and an integer $\ell$, is there an induced matching $M$ of size at
least $\ell$? An edge subset $M$ is an induced matching in $G$ if $M$ is a
matching such that there is no edge between two distinct edges of $M$. Our work
looks into the parameterized complexity of Induced Matching with respect to
"below guarantee" parameterizations. We consider the parameterization $u -
\ell$ for an upper bound $u$ on the size of any induced matching. For instance,
any induced matching is of size at most $n / 2$ where $n$ is the number of
vertices, which gives us a parameter $n / 2 - \ell$. In fact, there is a
straightforward $9^{n/2 - \ell} \cdot n^{O(1)}$-time algorithm for Induced
Matching [Moser and Thilikos, J. Discrete Algorithms]. Motivated by this, we
ask: Is Induced Matching FPT for a parameter smaller than $n / 2 - \ell$? In
search for such parameters, we consider $MM(G) - \ell$ and $IS(G) - \ell$,
where $MM(G)$ is the maximum matching size and $IS(G)$ is the maximum
independent set size of $G$. We find that Induced Matching is presumably not
FPT when parameterized by $MM(G) - \ell$ or $IS(G) - \ell$. In contrast to
these intractability results, we find that taking the average of the two helps
-- our main result is a branching algorithm that solves Induced Matching in
$49^{(MM(G) + IS(G))/ 2 - \ell} \cdot n^{O(1)}$ time. Our algorithm makes use
of the Gallai-Edmonds decomposition to find a structure to branch on.
