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 \(\mathcal {O}(n \log ^2 N)\) 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 \(\mathcal {O}(\Delta \log ^{7} N)\) 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 \(\mathcal {O}(n\log ^2 N +\Delta \log ^{7} N)\) with high probability