Bandwidth constrained multi-interface networks

In heterogeneous networks, devices can communicate by means of 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, and provides a communication bandwidth. In this paper, we consider the problem of activating the cheapest set of interfaces among a network G = (V,E) in order to guarantee a minimum bandwidth B of communication between two specified nodes. Nodes V represent the devices, edges E represent the connections that can be established. In practical cases, a bounded number k of different interfaces among all the devices can be considered. Despite this assumption, the problem turns out to be NP-hard even for small values of k and Δ, where Δ is the maximum degree of the network. In particular, the problem is NP-hard for any fixed k ≥ 2 and Δ ≥ 3, while it is polynomially solvable when k = 1, or Δ ≤ 2 and k = O(1). Moreover, we show that the problem is not approximable within ηlogB or Ω(loglog|V|) for any fixed k ≥ 3, Δ ≥ 3, and for a certain constant η, unless P=NP. We then provide an approximation algorithm with ratio guarantee of b max , where b max is the maximum communication bandwidth allowed among all the available interfaces. Finally, we focus on particular cases by providing complexity results and polynomial algorithms for Δ ≤ 2.