Distributed Bare-Bones Communication in Wireless Networks

Abstract: We consider wireless networks operating under the SINR model of interference. Nodes have limited individual knowledge and capabilities: they do not know their positions in a coordinate system in the plane, further they do not know their neighborhoods, nor do they know the size of the network $n$, and finally they cannot sense collisions resulting from simultaneous transmissions by at least two neighbors. Each node is equipped with a unique integer name, where $N$ as an upper bound on the a range of names. We refer as a backbone to a subnetwork induced by a diameter-preserving dominating set of nodes. Let $\Delta$ denote a maximum number of nodes that can successfully receive a message transmitted by a node when no other nodes transmit concurrently. We study distributed algorithms for communication problems in three settings. In the single-node-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 that wakes up all nodes in $O(n \log^2 N)$ rounds with high probability. For the synchronized-start case, when all nodes start an execution simultaneously, we give a randomized algorithm computing a backbone in $O(\Delta\log^{7} N)$ rounds with high probability. 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 in time $O(n\log^2 N +\Delta\log^{7} N)$ with high probability.