We consider the local broadcasting problem in the SINR model, which is a basic primitive for gathering initial information among @math wireless nodes. Assuming that nodes can measure received power, we achieve an essentially optimal constant approximate algorithm (with a @math additive term). This improves upon the previous best @math -approximate algorithm. Without power measurement, our algorithm achieves @math -approximation, matching the previous best result, but with a simpler approach that works under harsher conditions, such as arbitrary node failures. We give complementary lower bounds under reasonable assumptions.
Local broadcasting is related to the radio broadcasting problem in more classical models @cite_14 @cite_20 @cite_15 , to initialization and wake-up problems in wireless networks @cite_18 @cite_23 as well as coloring problems on disc graphs @cite_4 @cite_8 .
@cite_18 @cite_14 @cite_4 @cite_8 @cite_23 @cite_15 @cite_20
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The local broadcast problem assumes that processes in a wireless network are provided messages, one by one, that must be delivered to their neighbors. In this paper, we prove tight bounds for this problem in two well-studied wireless network models: the classical model, in which links are reliable and collisions consistent, and the more recent dual graph model, which introduces unreliable edges. Our results prove that the Decay strategy, commonly used for local broadcast in the classical setting, is optimal. They also establish a separation between the two models, proving that the dual graph setting is strictly harder than the classical setting, with respect to this primitive. The paper considers broadcasting in radio networks, modeled as unit disk graphs (UDG). Such networks occur in wireless communication between sites (e.g., stations or sensors) situated in a terrain. Network stations are represented by points in the Euclidean plane, where a station is connected to all stations at distance at most 1 from it. A message transmitted by a station reaches all its neighbors, but a station hears a message (receives the message correctly) only if exactly one of its neighbors transmits at a given time step. One station of the network, called the source, has a message which has to be disseminated to all other stations. Stations are unaware of the network topology. Two broadcasting models are considered. In the conditional wake up model, the stations other than the source are initially idle and cannot transmit until they hear a message for the first time. In the spontaneous wake up model, all stations are awake (and may transmit messages) from the beginning. It turns out that broadcasting time depends on two parameters of the UDG network, namely, its diameter D and its granularity g, which is the inverse of the minimum distance between any two stations. We present a deterministic broadcasting algorithm which works in time O (D g) under the conditional wake up model and prove that broadcasting in this model cannot be accomplished by any deterministic algorithm in time better than ( (D g ) ) . For the spontaneous wake up model, we design two deterministic broadcasting algorithms: the first works in time O (D + g 2) and the second in time O (D log g). While neither of these algorithms alone is optimal for all parameter values, we prove that the algorithm obtained by interleaving their steps, and thus working in time ( O ( D + g^2, D g ) ), turns out to be optimal by establishing a matching lower bound. The unstructured multi-hop radio network model, with asynchronous wake-up, no collision detection and little knowledge on the network topology, is proposed for capturing the particularly harsh characteristics of initially deployed wireless adhoc and sensor networks. In this paper, assuming such a practical model, we study a fundamental problem of both theoretical and practical interests--the local broadcasting problem. Given a set of nodes V where each node wants to broadcast a message to all its neighbors that are within a certain local broadcasting range R, the problem is to schedule all these requests in the fewest timeslots. By adopting the physical interference mode land without any knowledge on neighborhood, we give a new randomized distributed approximation algorithm for the local broadcasting problem with approximation ratio O (log n) where nis the number of nodes. This distributed approximation algorithm improves the state-of-the-art result in [22] by a logarithmic factor. Radio networks model wireless communication when processing units communicate using one wave frequency. This is captured by the property that multiple messages arriving simultaneously to a node interfere with one another and none of them can be read reliably. We present improved solutions to the problem of waking up such a network. This requires activating all nodes in a scenario when some nodes start to be active spontaneously, while every sleeping node needs to be awaken by receiving successfully a message from a neighbor. Our contributions concern the existence and efficient construction of universal radio synchronizers, which are combinatorial structures introduced in [6] as building blocks of efficient wake-up algorithms. First we show by counting that there are (n,g)-universal synchronizers for @math . Next we show an explicit construction of (n,g)-universal-synchronizers for @math . By way of applications, we obtain an existential wake-up algorithm which works in time @math and an explicitly instantiated algorithm that works in time @math , where n is the number of nodes and @math is the maximum in-degree in the network. Algorithms for leader-election and synchronization can be developed on top of wake-up ones, as shown in [7], such that they work in time slower by a factor of @math than the underlying wake-up ones.