Asynchronous Broadcasting with Bivalent Beeps

Abstract

In broadcasting, one node of a network has a message that must be learned by all other nodes. We study deterministic algorithms for this fundamental communication task in a very weak model of wireless communication. The only signals sent by nodes are beeps. Moreover, they are delivered to neighbors of the beeping node in an asynchronous way: the time between sending and reception is finite but unpredictable. We first observe that under this scenario, no communication is possible, if beeps are all of the same strength. Hence we study broadcasting in the bivalent beeping model, where every beep can be either soft or loud. At the receiving end, if exactly one soft beep is received by a node in a round, it is heard as soft. Any other combination of beeps received in a round is heard as a loud beep. The cost of a broadcasting algorithm is the total number of beeps sent by all nodes.We consider four levels of knowledge that nodes may have about the network: anonymity (no knowledge whatsoever), ad-hoc (all nodes have distinct labels and every node knows only its own label), neighborhood awareness (every node knows its label and labels of all neighbors), and full knowledge (every node knows the entire labeled map of the network and the identity of the source). We first show that in the anonymous case, broadcasting is impossible even for very simple networks. For each of the other three knowledge levels we provide upper and lower bounds on the minimum cost of a broadcasting algorithm. Our results show separations between all these scenarios. Perhaps surprisingly, the jump in broadcasting cost between the ad-hoc and neighborhood awareness levels is much larger than between the neighborhood awareness and full knowledge levels, although in the two former levels knowledge of nodes is local, and in the latter it is global.

Communicating with beeps

“…To our knowledge there have been no earlier published results for broadcast, gossiping, and multi-broadcast in the model we study. Further recent works explore other tasks in various related beeping models ( [2,3,12,14]).…”

“…There are several possible ways of modeling asynchronicity, and exploring what can be done in asynchronous beeping networks. One work in this direction is [14].…”

Distributed Voting in Beep Model

“…Although beep model is almost a newly developed communication protocol, it has been received much attention in recent years and various algorithms have been proposed for different distributed problems in this model. As examples of these problems, we can mention interval coloring and graph coloring [5], [14], [15], [16], leader election [17], [18], [19], [20], [21], [22], [23], maximal independent set [24], [25], [26], [27], [28], [29], minimum connected dominating set [30], network size approximation and counting [31], [32], [33], [34], deterministic rendezvous problem [35], naming problem [36], membership problem [37], [38], broadcasting [39], [40], [41], and consensus [42].…”

Naming a Channel with Beeps

“…Czumaj and Davies [23] approached systematically the tasks of deterministic broadcasting, gossiping, and multi-broadcasting on the bit level in general-topology symmetric beeping networks. In a related work, Hounkanli and Pelc [42] studied deterministic broadcasting in asynchronous beeping networks of general topology with various levels of knowledge about the network. Förster et al [34] considered leader election by deterministic algorithms in general multi-hop networks with beeping.…”