takes $O(c)$ time because $B_i$ contains at most $c$ arcs for any $i \in [n_S]$. In the update phase, we iterate over all vertices (), at most $c$ neighbors (), and all subsets of ${\mathcal{S}_{G,\ell}^{\operatorname{reach}}}(S)$ (). Each iteration takes $O(c)$ time because $D_i(\mathcal{T})$ contains at most $c$ arcs for any $i \in [n_S]$ and any $\mathcal{T} \subseteq {\mathcal{S}_{G,\ell}^{\operatorname{reach}}}(S)$. Thus, the overall running time is $O(2^c \cdot c^2 \cdot n)$.

#### Phase 3.

We finally present the search tree algorithm for <span style="font-variant:small-caps;">MinPAC</span> in . The algorithm “guesses” the connections between SCCs of $G_\ell$ to obtain an optimal solution. To this end, we first try all possible numbers of outgoing arcs from each SCC. The array $\mathcal{C}$ contains after \[mainend\] for each SCC $S_i$ in the $i$^th^ entry all SCCs that $S_i$ has an arc to in the solution.

\[fpt:parameterc\] Given a relevant subgraph ${G_\ell^{\operatorname{rel}}}$, a relevant weight function ${w_\ell^{\operatorname{rel}}}$, and a minimum-cost connector $\operatorname{MCC}\colon \mathcal{S}_{G_\ell} \times 2^{\mathcal{S}_{G_\ell}} \to 2^{A({G_\ell^{\operatorname{rel}}})}$, computes an optimal solution of $({G_\ell^{\operatorname{rel}}}, {w_\ell^{\operatorname{rel}}})$ in $O(n + m + 4^c \cdot c^{2c - 3/2})$ time.

We first show the correctness of . In each iteration step (), we construct an auxiliary graph $H^{\mathrm{aux}}$, which is basically a graph 