Min-Max Coverage in Multi-Interface Networks

We consider devices equipped with multiple wired or wireless interfaces. By switching among interfaces or by combining the available interfaces, each device might establish several connections. A connection is established when the devices at its endpoints share at least one active interface. Each interface is assumed to require an activation cost. In this paper, we consider the problem of establishing the connections defined by a network G = (V,E) while keeping as low as possible the maximum cost set of active interfaces at the single nodes. Nodes V represent the devices, edges E represent the connections that must be established. We study the problem of minimizing the maximum cost set of active interfaces among the nodes of the network in order to cover all the edges. We prove that the problem is NP-hard for any fixed Δ ≥ 5 and k ≥ 16, with Δ being the maximum degree, and k being the number of different interfaces among the network. We also show that the problem cannot be approximated within Ω(ln Δ). We then provide a general approximation algorithm which guarantees a factor of O((1 + b)ln (Δ)), with b being a parameter depending on the topology of the input graph. Interestingly, b can be bounded by a constant for many graph classes. Other approximation and exact algorithms for special cases are presented.