We consider networks of processes which interact with beeps. Various beeping models are used. The basic one, defined by Cornejo and Kuhn [CK10], assumes that a process can choose either to beep or to listen; if it listens it can distinguish between silence or the presence of at least one beep. The aim of this paper is the study of the resolution of paradigms such as collision detection, computation of the degree of a vertex, colouring, or 2-hop-colouring in the framework of beeping models. For each of these problems we present Las Vegas or Monte Carlo algorithms and we analyse their complexities expressed in terms of the number of slots. We present also efficient randomised emulations of more powerful beeping models on the basic one. We illustrate emulation procedures with an efficient degree computation algorithm in the basic beeping model; this algorithm was given initially in a more powerful model.
We present and analyse Las Vegas distributed algorithms which compute a MIS or a maximal matching for anonymous rings. Their bit complexity and time complexity are O(logn) with high probability. These algorithms are optimal modulo a multiplicative constant. Beyond the complexity results, the interest of this work stands in the description and the analysis of these algorithms which may be easily generalised. Furthermore, these results show a separation between the complexity of the MIS problem (and of the maximal matching problem) on the one hand and the colouring problem on the other. Colouring can be computed only in @W(logn) rounds on rings with high probability, while MIS is shown to have a faster algorithm. This is in contrast to other models, in which MIS is at least as hard as colouring.