Maximum Matching in Multi-Interface Networks

In heterogeneous networks, devices can communicate by means of multiple wireless interfaces. By choosing which interfaces to switch on at each device, several connections might be established. That is, the devices at the endpoints of each connection share at least one active interface. In this paper, we consider the standard matching problem in the context of multi-interface wireless networks. The aim is to maximize the number of parallel connections without incurring interferences. Given a network G=(V,E), nodes V represent the devices, and edges E represent the connections that can be established. If node x participates in the communication with one of its neighbors by means of interface i, then another neighboring node of x can establish a connection (but not with x) only if it makes use of interface j≠i. The size of a solution for an instance of the outcoming matching problem, which we call Maximum Matching in Multi-Interface networks (MMMI for short), is always in between the sizes of the solutions for the same instance with respect to the standard matching and its induced version problems. However, we prove that MMMI is NP-hard even for proper interval graphs and for bipartite graphs of maximum degree Δ≥3. We also show polynomially solvable cases of MMMI with respect to different assumptions.