Distributed Bare-Bones Communication in Wireless Networks

We consider wireless networks with the SINR model of interference when nodes have very limited individual knowledge and capabilities. In particular, nodes do not know their geographic coordinates and their neighborhoods, nor even the size $n$ of the network, nor can they sense collisions. Each node is equipped only with a unique integer name, where $N$ is an upper bound on their range. We study distributed algorithms for communication problems in the following three settings. In the single-node-start case, when one node starts an execution and the other nodes are awoken by receiving messages from already awoken nodes, we present a randomized broadcast algorithm which wakes up all the nodes in $O(n \log^2 N)$ rounds with high probability. Let $\Delta$ denote the maximum number of nodes that successfully receive a message transmitted by a node when no other nodes transmit. For the synchronized-start case, when all the nodes start an execution simultaneously, we give a randomized algorithm that computes a backbone of the network in $O(\Delta\log^{7} N)$ rounds with high probability. Finally, in the partly-coordinated-start case, when a number of nodes start an execution together and other nodes are awoken by receiving messages from the already awoken nodes, we develop an algorithm that creates a backbone network in time $O(n\log^2 N +\Delta\log^{7} N)$ with high probability.