16 research outputs found

    Information Gathering in Ad-Hoc Radio Networks with Tree Topology

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    We study the problem of information gathering in ad-hoc radio networks without collision detection, focussing on the case when the network forms a tree, with edges directed towards the root. Initially, each node has a piece of information that we refer to as a rumor. Our goal is to design protocols that deliver all rumors to the root of the tree as quickly as possible. The protocol must complete this task within its allotted time even though the actual tree topology is unknown when the computation starts. In the deterministic case, assuming that the nodes are labeled with small integers, we give an O(n)-time protocol that uses unbounded messages, and an O(n log n)-time protocol using bounded messages, where any message can include only one rumor. We also consider fire-and-forward protocols, in which a node can only transmit its own rumor or the rumor received in the previous step. We give a deterministic fire-and- forward protocol with running time O(n^1.5), and we show that it is asymptotically optimal. We then study randomized algorithms where the nodes are not labelled. In this model, we give an O(n log n)-time protocol and we prove that this bound is asymptotically optimal

    An O(n 1.5 ) Deterministic Gossiping Algorithm for Radio Networks

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    Gossip Algorithms for Distributed Signal Processing

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    Gossip algorithms are attractive for in-network processing in sensor networks because they do not require any specialized routing, there is no bottleneck or single point of failure, and they are robust to unreliable wireless network conditions. Recently, there has been a surge of activity in the computer science, control, signal processing, and information theory communities, developing faster and more robust gossip algorithms and deriving theoretical performance guarantees. This article presents an overview of recent work in the area. We describe convergence rate results, which are related to the number of transmitted messages and thus the amount of energy consumed in the network for gossiping. We discuss issues related to gossiping over wireless links, including the effects of quantization and noise, and we illustrate the use of gossip algorithms for canonical signal processing tasks including distributed estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page

    Information gathering in ad-hoc radio networks with tree topology

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    We study the problem of information gathering in ad-hoc radio networks, focusing on the case when the network forms a tree, with edges directed towards the root. Initially, each node has a rumor, and we aim to deliver all rumors to the root as quickly as possible without knowing the tree's topology in advance. In the deterministic case, where nodes are labeled with small integers, we give an -time protocol for the model with unbounded message size, and an -time protocol for bounded message size. We also consider fire-and-forward protocols, in which nodes can transmit only their own rumor or the rumor received in the previous step. We give a deterministic fire-and-forward protocol with running time , and show that it is asymptotically optimal. We also present a randomized -time protocol in the model without node labels or aggregation, and show that it is asymptotically optimal

    Geographic Gossip: Efficient Averaging for Sensor Networks

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    Gossip algorithms for distributed computation are attractive due to their simplicity, distributed nature, and robustness in noisy and uncertain environments. However, using standard gossip algorithms can lead to a significant waste in energy by repeatedly recirculating redundant information. For realistic sensor network model topologies like grids and random geometric graphs, the inefficiency of gossip schemes is related to the slow mixing times of random walks on the communication graph. We propose and analyze an alternative gossiping scheme that exploits geographic information. By utilizing geographic routing combined with a simple resampling method, we demonstrate substantial gains over previously proposed gossip protocols. For regular graphs such as the ring or grid, our algorithm improves standard gossip by factors of nn and n\sqrt{n} respectively. For the more challenging case of random geometric graphs, our algorithm computes the true average to accuracy ϵ\epsilon using O(n1.5lognlogϵ1)O(\frac{n^{1.5}}{\sqrt{\log n}} \log \epsilon^{-1}) radio transmissions, which yields a nlogn\sqrt{\frac{n}{\log n}} factor improvement over standard gossip algorithms. We illustrate these theoretical results with experimental comparisons between our algorithm and standard methods as applied to various classes of random fields.Comment: To appear, IEEE Transactions on Signal Processin

    Gossip along the way: order-optimal consensus through randomized path averaging

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    Gossip algorithms have recently received significant attention, mainly because they constitute simple and robust algorithms for distributed information processing over networks. However for many topologies that are realistic for wireless ad-hoc and sensor networks (like grids and random geometric graphs), the standard nearest-neighbor gossip converges very slowly. A recently proposed algorithm called geographic gossip improves gossip efficiency by a n/logn\sqrt{n / \log n} factor for random geometric graphs, by exploiting geographic information of node locations. In this paper we prove that a variation of geographic gossip that averages along routed paths, improves efficiency by an additional n/logn\sqrt{n / \log n} factor and is order optimal for grids and random geometric graphs. Our analysis provides some general techniques and can be used to provide bounds on the performance of randomized message passing algorithms operating over various graph topologies
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