$p-Hitting-Set ≤fpt p-Dominating-Set$ (Flum–Grohe, Example 2.7). On the word of $(P, k)$ with $k ≤ n$ and no empty set, the reduction writes the graph of the compressed instance — its elements (the first occurrences of the members and $min k m$ spare elements) form a clique, and each set is a vertex joined to its elements — with parameter $min k m$; otherwise a fixed no-instance. The new parameter is at most $k + 1$, and an IMP+ program computes the reduction within $100000 (|x| + 1)^3$ steps.