Distributed Communication in Bare-Bones Wireless Networks

We consider wireless networks in which the effects of interference are determined by the SINR model. We address the question of structuring distributed communication when stations have very limited individual capabilities. In particular, nodes do not know their geographic coordinates, neighborhoods or even the size~$n$ of the network, nor can they sense collisions. Each node is equipped only with its unique name from a range $\{1, \dots, N\}$. We study the following three settings and distributed algorithms for communication problems in each of them. In the uncoordinated-start case, when one node starts an execution and 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. In the synchronized-start case, when all the nodes simultaneously start an execution, 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.