Radio networks are a long-studied model for distributed system of devices which communicate wirelessly. When these devices are mobile or have limited capabilities, the system is often best modeled by the ad-hoc variant, in which the devices do not know the structure of the network. A large body of work has been devoted to designing algorithms for the ad-hoc model, particularly for fundamental communications tasks such as broadcasting. Most of these algorithms, however, assume that devices have some network knowledge (usually bounds on the number of nodes in the network @math , and the diameter @math ), which may not always be realistic in systems with weak devices or gradual deployment. Very little is known about what can be done when this information is not available. This is the issue we address in this work, by presenting the first broadcasting algorithms for networks in which nodes have no prior knowledge whatsoever. We demonstrate that lack of parameter knowledge can be overcome at only a small increase in running time. Specifically, we show that in networks without collision detection, broadcast can be achieved in @math time, almost reaching the @math lower bound. We also give an algorithm for directed networks with collision detection, which requires only @math time.
Deterministic algorithms for broadcasting have also been studied; for undirected networks the fastest known algorithm is the @math -time algorithm of @cite_7 , while for directed networks it is the @math -time algorithm of @cite_3 .
@cite_3 @cite_7
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In this paper we improve the deterministic complexity of two fundamental communication primitives in the classical model of ad hoc radio networks with unknown topology: broadcasting and wake-up. We consider an unknown radio network, in which all nodes have no prior knowledge about network topology, and know only the size of the network @math , the maximum in-degree of any node @math , and the eccentricity of the network @math . For such networks, we first give an algorithm for wake-up, based on the existence of small universal synchronizers. This algorithm runs in @math time, the fastest known in both directed and undirected networks, improving over the previous best @math -time result across all ranges of parameters, but particularly when maximum in-degree is small. Next, we introduce a new combinatorial framework of block synchronizers and prove the existence of such objects of low size. Using this framework, we design a new deterministic ... We consider the time of broadcasting in ad hoc radio networks modeled as undirected graphs. In such networks, every node knows only its own label and a linear bound on the number of nodes but is unaware of the topology of the network, or even of its own neighborhood. Our aim is to study to what extent the availability of two important characteristics of a broadcasting algorithm influences optimal broadcasting time. These characteristics are adaptiveness and randomization. Our contribution is establishing upper and lower bounds on optimal broadcasting time for three classes of algorithms: adaptive deterministic, oblivious randomized and oblivious deterministic. In two cases we present tight bounds, and in one case a small gap remains. We show that for deterministic adaptive algorithms time Ω(n) is required even for n-node networks of constant diameter. This lower bound is strongest possible, since linear time algorithms are known, and hence establishes optimal time Θ(n) for this class. For oblivious randomized algorithms we show an upper bound O(n min D, log n ) and a lower bound Ω(n) on optimal expected broadcasting time in n-node networks of diameter D. Finally, for oblivious deterministic algorithms we show matching upper and lower bounds Θ(n min D, √n ) on optimal broadcasting time. Our results imply that enforcing obliviousness has at least as strong negative impact on broadcasting time as enforcing determinism, and that algorithms having both these features are strictly less efficient than those having only one of them. We establish an O(nlog2n) upper bound on the time for deterministic distributed broadcasting in multi-hop radio networks with unknown topology. This nearly matches the known lower bound of Ω(n log n). The fastest previously known algorithm for this problem works in time O(n3 2). Using our broadcasting algorithm, we develop an O(n3 2log2n) algorithm for gossiping in the same network model. We consider distributed broadcasting in radio networks, modeled as undirected graphs, whose nodes have no information on the topology of the network, nor even on their immediate neighborhood. For randomized broadcasting, we give an algorithm working in expected time O(D log(n D) + log2 n) in n-node radio networks of diameter D, which is optimal, as it matches the lower bounds of [1] and Kushilevitz and Mansour [14]. Our algorithm improves the best previously known randomized broadcasting algorithm of Bar-Yehuda, Goldreich and Itai [3], running in expected time O(D log n + log2 n). For deterministic broadcasting, we show the lower bound Ω(n(log n) (log (n D)))) on broadcasting time in n-node radio networks of diameter D. This implies previously known lower bounds of Bar-Yehuda, Goldreich and Itai [3] and Bruschi and Del Pinto [5], and is sharper than any of them in many cases. We also give an algorithm working in time O(n log n), thus shrinking -- for the first time -- the gap between the upper and the lower bound on deterministic broadcasting time to a logarithmic factor.