by the number of power levels {#sec:vcn}
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It is fair to assume that the nodes cannot transmit signals with arbitrary power levels due to practical limitations [@Carmi2007]. In fact, many researchers have studied approximation algorithms for the <span style="font-variant:small-caps;">MinPAC</span> problem when only two power levels are available [@Rong2004; @Carmi2007; @Calinescu2013approximate; @Calinescu2016]. In this section, we consider the case ${w \colon A(G) \to Q}$, where the set of integers $Q = \{ p_1, \dots, p_q \}$ represents available power levels. The parameter $q$—“the number of numbers”—has been advocated by @FGR12. The problem remains NP-hard even when $q = 2$ [@chen1989strongly], as also can be seen in our hardness result (). Thus, fixed-parameter tractability is unlikely with this parameter alone. However, using an additional parameter may alleviate this problem. We consider the *vertex cover number*, as many problems are known to become tractable when this parameter is bounded. Here we define the vertex cover number for a directed graph as the vertex cover number of the underlying undirected graph. Recall that the vertex cover number for an undirected graph is the minimum number of vertices that have to be removed to make it edgeless. Computing a minimum-cardinality vertex cover is NP-hard 