Some modern networks are set up using highly heterogeneous wireless devices. To make them work properly, selecting a subset of the available interfaces is required. This practical problem can be described by one of the well-known Multi-Interface network models. Among them is the Coverage model, where the main goal is to activate the cheapest subset of interfaces to establish all the desired links. Here, “cheapest" refers to energy consumption. This work focuses on the well-known Coverage in Multi-Interface network model. The network is represented by an undirected graph \(G = (V, E)\) , where each node corresponds to a device and each edge denotes a desired connection. Additionally, each node is equipped with a set of interfaces, and the objective is to find a subset of them such that every node has at least one common interface, minimizing the total energy cost. Since this problem has been proven to be NP-hard, we decided to analyze the case with respect to the dimension of the cycle space of G. Specifically, we provided a deterministic algorithm that returns a solution for the decision version of the problem, running in FPT-time relative to the sum of the number of available interfaces and the dimension of the cycle space.