14,834 research outputs found

    The Energy Complexity of Broadcast

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    Energy is often the most constrained resource in networks of battery-powered devices, and as devices become smaller, they spend a larger fraction of their energy on communication (transceiver usage) not computation. As an imperfect proxy for true energy usage, we define energy complexity to be the number of time slots a device transmits/listens; idle time and computation are free. In this paper we investigate the energy complexity of fundamental communication primitives such as broadcast in multi-hop radio networks. We consider models with collision detection (CD) and without (No-CD), as well as both randomized and deterministic algorithms. Some take-away messages from this work include: 1. The energy complexity of broadcast in a multi-hop network is intimately connected to the time complexity of leader election in a single-hop (clique) network. Many existing lower bounds on time complexity immediately transfer to energy complexity. For example, in the CD and No-CD models, we need Ω(logn)\Omega(\log n) and Ω(log2n)\Omega(\log^2 n) energy, respectively. 2. The energy lower bounds above can almost be achieved, given sufficient (Ω(n)\Omega(n)) time. In the CD and No-CD models we can solve broadcast using O(lognloglognlogloglogn)O(\frac{\log n\log\log n}{\log\log\log n}) energy and O(log3n)O(\log^3 n) energy, respectively. 3. The complexity measures of Energy and Time are in conflict, and it is an open problem whether both can be minimized simultaneously. We give a tradeoff showing it is possible to be nearly optimal in both measures simultaneously. For any constant ϵ>0\epsilon>0, broadcast can be solved in O(D1+ϵlogO(1/ϵ)n)O(D^{1+\epsilon}\log^{O(1/\epsilon)} n) time with O(logO(1/ϵ)n)O(\log^{O(1/\epsilon)} n) energy, where DD is the diameter of the network

    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

    Distributed Deterministic Broadcasting in Uniform-Power Ad Hoc Wireless Networks

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    Development of many futuristic technologies, such as MANET, VANET, iThings, nano-devices, depend on efficient distributed communication protocols in multi-hop ad hoc networks. A vast majority of research in this area focus on design heuristic protocols, and analyze their performance by simulations on networks generated randomly or obtained in practical measurements of some (usually small-size) wireless networks. %some library. Moreover, they often assume access to truly random sources, which is often not reasonable in case of wireless devices. In this work we use a formal framework to study the problem of broadcasting and its time complexity in any two dimensional Euclidean wireless network with uniform transmission powers. For the analysis, we consider two popular models of ad hoc networks based on the Signal-to-Interference-and-Noise Ratio (SINR): one with opportunistic links, and the other with randomly disturbed SINR. In the former model, we show that one of our algorithms accomplishes broadcasting in O(Dlog2n)O(D\log^2 n) rounds, where nn is the number of nodes and DD is the diameter of the network. If nodes know a priori the granularity gg of the network, i.e., the inverse of the maximum transmission range over the minimum distance between any two stations, a modification of this algorithm accomplishes broadcasting in O(Dlogg)O(D\log g) rounds. Finally, we modify both algorithms to make them efficient in the latter model with randomly disturbed SINR, with only logarithmic growth of performance. Ours are the first provably efficient and well-scalable, under the two models, distributed deterministic solutions for the broadcast task.Comment: arXiv admin note: substantial text overlap with arXiv:1207.673

    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

    Message and time efficient multi-broadcast schemes

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    We consider message and time efficient broadcasting and multi-broadcasting in wireless ad-hoc networks, where a subset of nodes, each with a unique rumor, wish to broadcast their rumors to all destinations while minimizing the total number of transmissions and total time until all rumors arrive to their destination. Under centralized settings, we introduce a novel approximation algorithm that provides almost optimal results with respect to the number of transmissions and total time, separately. Later on, we show how to efficiently implement this algorithm under distributed settings, where the nodes have only local information about their surroundings. In addition, we show multiple approximation techniques based on the network collision detection capabilities and explain how to calibrate the algorithms' parameters to produce optimal results for time and messages.Comment: In Proceedings FOMC 2013, arXiv:1310.459

    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
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