We consider networks of processes which interact with beeps. In the basic model defined by Cornejo and Kuhn, which we refer to as the BL variant, processes can choose in each round either to beep or to listen. Those who beep are unable to detect simultaneous beeps. Those who listen can only distinguish between silence and the presence of at least one beep. Stronger variants exist where the nodes can also detect collision while they are beeping (B_{cd}L) or listening (BL_{cd}), or both (B_{cd}L_{cd}). Beeping models are weak in essence and even simple tasks are difficult or unfeasible with them. This paper starts with a discussion on generic building blocks (design patterns) which seem to occur frequently in the design of beeping algorithms. They include multi-slot phases: the fact of dividing the main loop into a number of specialised slots; exclusive beeps: having a single node beep at a time in a neighbourhood (within one or two hops); adaptive probability: increasing or decreasing the probability of beeping to produce more exclusive beeps; internal (resp. peripheral) collision detection: for detecting collision while beeping (resp. listening); and emulation of collision detection: for enabling this feature when it is not available as a primitive. We then provide algorithms for a number of basic problems, including colouring, 2-hop colouring, degree computation, 2-hop MIS, and collision detection (in BL). Using the patterns, we formulate these algorithms in a rather concise and elegant way. Their analyses (in the full version) are more technical, e.g. one of them relies on a Martingale technique with non-independent variables; another improves that of the MIS algorithm (P. Jeavons et al.) by getting rid of a gigantic constant (the asymptotic order was already optimal). Finally, we study the relative power of several variants of beeping models. In particular, we explain how every Las Vegas algorithm with collision detection can be converted, through emulation, into a Monte Carlo algorithm without, at the cost of a logarithmic slowdown. We prove that this slowdown is optimal up to a constant factor by giving a matching lower bound.

We address the enumeration and the leader election problems over partially anonymous and multi-hop broadcast networks. We consider an asynchronous communication model where each process broadcasts a message and all its neighbours receive this message after arbitrary and unpredictable time. In this paper, we present necessary conditions that must be satisfied by any graph to solve these problems and we show that these conditions are sufficient by providing an enumeration algorithm on the one hand and a leader election algorithm on the other hand. For both problems, we highlight the importance of the initial knowledge. Considering the enumeration problem, each process only knows the size of the graph and, contrary to related works, the number of its neighbouring processes is unknown. Whereas for the election problem, we show that this combination of knowledge is not sufficient. Our algorithm assumes that each process initially knows a map of the network (without knowing its position in this map). From the complexity viewpoint, our algorithms offer polynomial complexities (memory at each process, number and size of exchanged messages).

Needless to say, distributed algorithms are usually hard to design mush harder to prove and to use in real distributed systems. In these systems, local computations theory has proved its power to formalize and prove in an intuitive way distributed algorithms. This paper uses this formalism to present solutions to the election problem in several network topologies using mobile agents at the design and the implementation levels. We formalized the proposed solutions in the local computations model using transition systems [11]. This facilitates the proof of the proposed solutions using the mathematical tool-box provided by the local computation theory. Using mobile agents, the proposed solutions get rid of synchronization and do not need continuous use of all machines computational resources. Proposed solutions are also simulated within the VISIDIA [3] platform.