A new kind of selectors and their applications to conflict resolution in wireless multichannels networks

We investigate the benefits of using multiple channels in wireless networks, under the full-duplex multi-packet reception model of communication. The main question we address is the following: Is a speedup linear in the number of channels available, for some interesting communication primitive? We provide a positive answer to this interrogative for the Information Exchange Problem, in which up to k arbitrary nodes have information they intend to share with the entire network. In particular, we give non-adaptive deterministic protocols for both the scenario in which the channels provide the transmitting stations with the feedback on whether their transmissions have been successful and for the scenario in which channels provide no such feedback. To this aim, we devise and exploit a new combinatorial structure that generalizes well known combinatorial tools, widely used in the area of data-exchange in multiple-access channels (i.e., strongly selective families, selectors, and related mathematical objects). For our new combinatorial structures we provide both existential results and randomized algorithms to generate them. We also prove non-existence results showing that our protocol for the model with feedback is optimal, whereas that for the no-feedback scenario uses a number of time slots that exceeds the lower bound by a log⁡k factor. Leveraging on properties of error correcting codes, we show that for an infinite set of the relevant parameters n and k, one can construct our combinatorial structure for the no-feedback scenario in polynomial time and of minimum length.