Multi-Broadcasting under the SINR Model.

We study the multi-broadcast problem in multi-hop wireless networks under the SINR model deployed in the 2D Euclidean plane. In multi-broadcast, there are $k$ initial rumours, potentially belonging to different nodes, that must be forwarded to all $n$ nodes of the network. Furthermore, in each round a node can only transmit a small message that could contain at most one initial rumor and $O(\log n)$ control bits. In order to be successfully delivered to a node, transmissions must satisfy the (Signal-to-Inference-and-Noise-Ratio) SINR condition and have sufficiently strong signal at the receiver. We present deterministic algorithms for multi-broadcast for different settings that reflect the different types of knowledge about the topology of the network available to the nodes: (i) the whole network topology (ii) their own coordinates and coordinates of their neighbors (iii) only their own coordinates, and (iv) only their own ids and the ids of their neighbors. For the former two settings, we present solutions that are scalable with respect to the diameter of the network and the polylogarithm of the network size, i.e., $\log^c n$ for some constant $c> 0$, while the solutions for the latter two have round complexity that is superlinear in the number of nodes. The last result is of special significance, as it is the first result for the SINR model that does not require nodes to know their coordinates in the plane (a very specialized type of knowledge), but intricately exploits the understanding that nodes are implanted in the 2D Euclidean plane.