Efficient Broadcast on Random Geometric Graphs

Bradonjic, Milan; Elsässer, Robert; Friedrich, Tobias; Sauerwald, Thomas; Stauffer, Alexandre

doi:10.1137/1.9781611973075.114

Cited by 28 publications

(38 citation statements)

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“…Taking K and K appearing in Proposition 5.1 to be K = 2L and K = L, we see by the choice of Δ that for large enough t the condition for K in Proposition 5.1 is satisfied and thus we obtain, uniformly over all F ∈ F i , that, for a positive constant c 6 ,…”

Section: Percolation Timementioning

confidence: 99%

“…The question of broadcasting within the giant component of a RGG above the percolation threshold was recently analyzed by Bradonjić et al [6], who also show that the graph distance between any two (sufficiently distant) nodes is at most a constant factor larger than their Euclidean distance. Cover times for random walks on (connected) RGGs were investigated by Avin and Ercal [2] and Cooper and Frieze [9], while the effect of physical obstacles that obstruct transmission was studied by Frieze et al [15].…”

Section: Motivation and Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Mobile Geometric Graphs: Detection, Coverage and Percolation

Peres¹,

Sinclair²,

Sousi³

et al. 2011

Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms

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Static wireless networks are by now quite well understood mathematically through the random geometric graph model. By contrast, there are relatively few rigorous results on the practically important case of mobile networks. In this paper we consider a natural extension of the random geometric graph model to the mobile setting by allowing nodes to move in space according to Brownian motion. We study three fundamental questions in this model: detection (the time until a given target point-which may be either fixed or moving-is detected by the network), coverage (the time until all points inside a finite box are detected by the network), and percolation (the time until a given node is able to communicate with the giant component of the network). We derive precise asymptotics for these problems by combining ideas from stochastic geometry, coupling and multi-scale analysis. We also give an application of our results to analyze the time to broadcast a message in a mobile network.

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Section: Percolation Timementioning

confidence: 99%

Section: Motivation and Related Workmentioning

confidence: 99%

Mobile Geometric Graphs: Detection, Coverage and Percolation

Peres¹,

Sinclair²,

Sousi³

et al. 2011

Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms

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“…Krishnan et al [6] and Krzywdziński and Rybarczyk [18] describe results for the probability of connectivity asymptotically converging to 1 in WSNs employing the q-composite key predistribution scheme with q = 1 (i.e., the basic EschenauerGligor key predistribution scheme [1]), not under the on/off channel model but under the well-known disk model [17], [23], [33], [35], [39], [42], where nodes are distributed over a bounded region of a Euclidean plane, and two nodes have to be within a certain distance for communication. Simulation results in our work [44] indicate that for WSNs under the key predistribution scheme with q = 1, when the on-off channel model is replaced by the disk model, the performances for kconnectivity and for the property that the minimum degree is at least k do not change significantly.…”

Section: Related Workmentioning

confidence: 99%

On topological properties of wireless sensor networks under the q-composite key predistribution scheme with on/off channels

Zhao

Yağan

Gligor

2014

2014 IEEE International Symposium on Information Theory

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The q-composite key predistribution scheme [2] is used prevalently for secure communications in large-scale wireless sensor networks (WSNs). Prior work [5], [13], [44] explores topological properties of WSNs employing the q-composite scheme for q = 1 with unreliable communication links modeled as independent on/off channels. In this paper, we investigate topological properties related to the node degree in WSNs operating under the q-composite scheme and the on/off channel model. Our results apply to general q and are stronger than those reported for the node degree in prior work even for the case of q being 1. Specifically, we show that the number of nodes with an arbitrary degree asymptotically converges to a Poisson distribution, present the asymptotic probability distribution for the minimum degree of the network, and establish the asymptotically exact probability for the property that the minimum degree is at least an arbitrary value. Numerical experiments confirm the validity of our analytical findings.

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“…Additional recent work includes the work of Bradonjić et al [6], who analyze information spreading in random geometric graphs, and the work of Georgiou et al [15], studying information spreading in asynchronous networks. Sarwate and Dimakis [24] and Boyd et al [5] study the problem in wireless sensor networks.…”

Section: Related Workmentioning

confidence: 99%

Fast Information Spreading in Graphs with Large Weak Conductance

Censor-Hillel¹,

Shachnai²

2012

SIAM J. Comput.

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Gathering data from nodes in a network is at the heart of many distributed applications, most notably, while performing a global task. We consider information spreading among n nodes of a network, where each node v has a message m(v) which must be received by all other nodes. The time required for information spreading has been previously upper-bounded with an inverse relationship to the conductance of the underlying communication graph. This implies high running times for graphs with small conductance.The main contribution of this paper is an information spreading algorithm which overcomes communication bottlenecks and thus achieves fast information spreading for a wide class of graphs, despite their small conductance. As a key tool in our study we use the recently defined concept of weak conductance, a generalization of classic graph conductance which measures how well-connected the components of a graph are. Our hybrid algorithm, which alternates between random and deterministic communication phases, exploits the connectivity within components by first applying partial information spreading, after which messages are sent across bottlenecks, thus spreading further throughout the network. This yields substantial improvements over the best known running times of algorithms for information spreading on any graph that has a large weak conductance, from polynomial to polylogarithmic number of rounds.We demonstrate the power of fast information spreading in accomplishing global tasks on the leader election problem, which lies at the core of distributed computing. Our results yield an algorithm for leader election that has a scalable running time on graphs with large weak conductance, improving significantly upon previous results.

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Efficient Broadcast on Random Geometric Graphs

Cited by 28 publications

References 0 publications

Mobile Geometric Graphs: Detection, Coverage and Percolation

Mobile Geometric Graphs: Detection, Coverage and Percolation

On topological properties of wireless sensor networks under the q-composite key predistribution scheme with on/off channels

Fast Information Spreading in Graphs with Large Weak Conductance

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