20,820 research outputs found

    Achieving Dilution without Knowledge of Coordinates in the SINR Model

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    Considerable literature has been developed for various fundamental distributed problems in the SINR (Signal-to-Interference-plus-Noise-Ratio) model for radio transmission. A setting typically studied is when all nodes transmit a signal of the same strength, and each device only has access to knowledge about the total number of nodes in the network nn, the range from which each node's label is taken [1,,N][1,\dots,N], and the label of the device itself. In addition, an assumption is made that each node also knows its coordinates in the Euclidean plane. In this paper, we create a technique which allows algorithm designers to remove that last assumption. The assumption about the unavailability of the knowledge of the physical coordinates of the nodes truly captures the `ad-hoc' nature of wireless networks. Previous work in this area uses a flavor of a technique called dilution, in which nodes transmit in a (predetermined) round-robin fashion, and are able to reach all their neighbors. However, without knowing the physical coordinates, it's not possible to know the coordinates of their containing (pivotal) grid box and seemingly not possible to use dilution (to coordinate their transmissions). We propose a new technique to achieve dilution without using the knowledge of physical coordinates. This technique exploits the understanding that the transmitting nodes lie in 2-D space, segmented by an appropriate pivotal grid, without explicitly referring to the actual physical coordinates of these nodes. Using this technique, it is possible for every weak device to successfully transmit its message to all of its neighbors in Θ(lgN)\Theta(\lg N) rounds, as long as the density of transmitting nodes in any physical grid box is bounded by a known constant. This technique, we feel, is an important generic tool for devising practical protocols when physical coordinates of the nodes are not known.Comment: 10 page

    Deterministic Communication in Radio Networks

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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 nn, the maximum in-degree of any node Δ\Delta, and the eccentricity of the network DD. For such networks, we first give an algorithm for wake-up, based on the existence of small universal synchronizers. This algorithm runs in O(min{n,DΔ}lognlogΔloglogΔ)O(\frac{\min\{n, D \Delta\} \log n \log \Delta}{\log\log \Delta}) time, the fastest known in both directed and undirected networks, improving over the previous best O(nlog2n)O(n \log^2n)-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 algorithm for the fundamental problem of broadcasting, running in O(nlogDloglogDΔn)O(n \log D \log\log\frac{D \Delta}{n}) time. This is the fastest known algorithm for the problem in directed networks, improving upon the O(nlognloglogn)O(n \log n \log \log n)-time algorithm of De Marco (2010) and the O(nlog2D)O(n \log^2 D)-time algorithm due to Czumaj and Rytter (2003). It is also the first to come within a log-logarithmic factor of the Ω(nlogD)\Omega(n \log D) lower bound due to Clementi et al.\ (2003). Our results also have direct implications on the fastest \emph{deterministic leader election} and \emph{clock synchronization} algorithms in both directed and undirected radio networks, tasks which are commonly used as building blocks for more complex procedures

    Faster Gossiping in Bidirectional Radio Networks with Large Labels

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    We consider unknown ad-hoc radio networks, when the underlying network is bidirectional and nodes can have polynomially large labels. For this model, we present a deterministic protocol for gossiping which takes O(nlg2nlglgn)O(n \lg^2 n \lg \lg n) rounds. This improves upon the previous best result for deterministic gossiping for this model by [Gasienec, Potapov, Pagourtizis, Deterministic Gossiping in Radio Networks with Large labels, ESA (2002)], who present a protocol of round complexity O(nlg3nlglgn)O(n \lg^3 n \lg \lg n) for this problem. This resolves open problem posed in [Gasienec, Efficient gossiping in radio networks, SIROCCO (2009)], who cite bridging gap between lower and upper bounds for this problem as an important objective. We emphasize that a salient feature of our protocol is its simplicity, especially with respect to the previous best known protocol for this problem

    Bounds on Contention Management in Radio Networks

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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

    Deterministic Digital Clustering of Wireless Ad Hoc Networks

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    We consider deterministic distributed communication in wireless ad hoc networks of identical weak devices under the SINR model without predefined infrastructure. Most algorithmic results in this model rely on various additional features or capabilities, e.g., randomization, access to geographic coordinates, power control, carrier sensing with various precision of measurements, and/or interference cancellation. We study a pure scenario, when no such properties are available. As a general tool, we develop a deterministic distributed clustering algorithm. Our solution relies on a new type of combinatorial structures (selectors), which might be of independent interest. Using the clustering, we develop a deterministic distributed local broadcast algorithm accomplishing this task in O(ΔlogNlogN)O(\Delta \log^*N \log N) rounds, where Δ\Delta is the density of the network. To the best of our knowledge, this is the first solution in pure scenario which is only polylog(n)(n) away from the universal lower bound Ω(Δ)\Omega(\Delta), valid also for scenarios with randomization and other features. Therefore, none of these features substantially helps in performing the local broadcast task. Using clustering, we also build a deterministic global broadcast algorithm that terminates within O(D(Δ+logN)logN)O(D(\Delta + \log^* N) \log N) rounds, where DD is the diameter of the network. This result is complemented by a lower bound Ω(DΔ11/α)\Omega(D \Delta^{1-1/\alpha}), where α>2\alpha > 2 is the path-loss parameter of the environment. This lower bound shows that randomization or knowledge of own location substantially help (by a factor polynomial in Δ\Delta) in the global broadcast. Therefore, unlike in the case of local broadcast, some additional model features may help in global broadcast
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