Lower Bounds for Noisy Wireless Networks using Sampling Algorithms

Dutta, Chinmoy; Radhakrishnan, Jaikumar

doi:10.1109/focs.2008.72

Cited by 8 publications

(7 citation statements)

References 12 publications

(18 reference statements)

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“…However, no non-trivial lower bound that apply specifically to communication networks with limited transmission radius had appeared in the literature before this work. Subsequent to the initial presentation of this work [2], Dutta and Radhakrishnan [3] showed that the same lower bound of Ω(N log log N ) holds for computing a host of boolean functions including the majority function.…”

Section: Related Workmentioning

confidence: 97%

How Hard is Computing Parity with Noisy Communications?

Dutta,

Kanoria,

Manjunath

et al. 2015

Preprint

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We show a tight lower bound of Ω(N log log N ) on the number of transmissions required to compute the parity of N input bits with constant error in a noisy communication network of N randomly placed sensors, each having one input bit and communicating with others using local transmissions with power near the connectivity threshold. This result settles the lower bound question left open by Ying, Srikant and Dullerud (WiOpt 06), who showed how the sum of all the N bits can be computed using O(N log log N ) transmissions. The same lower bound has been shown to hold for a host of other functions including majority by Dutta and Radhakrishnan (FOCS 2008).Most works on lower bounds for communication networks considered mostly the full broadcast model without using the fact that the communication in real networks is local, determined by the power of the transmitters. In fact, in full broadcast networks computing parity needs θ(N ) transmissions. To obtain our lower bound we employ techniques developed by Goyal, Kindler and Saks (FOCS 05), who showed lower bounds in the full broadcast model by reducing the problem to a model of noisy decision trees. However, in order to capture the limited range of transmissions in real sensor networks, we adapt their definition of noisy decision trees and allow each node of the tree access to only a limited part of the input. Our lower bound is obtained by exploiting special properties of parity computations in such noisy decision trees.

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Section: Related Workmentioning

confidence: 97%

How Hard is Computing Parity with Noisy Communications?

Dutta,

Kanoria,

Manjunath

et al. 2015

Preprint

Self Cite

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“…Research has shown that the answer depends crucially on the computational model in question. Models studied in this context include decision trees [21,43,19,17,38], circuits [40,22,18,30,52,53], broadcast networks [23,36,20,38,25,14,15], and communication protocols [45,46,7,24]. Some computational models exhibit a surprising degree of robustness to noise, in that one can compute the correct answer with probability 99% with only a constant-factor increase in cost relative to the noise-free setting.…”

Section: Introductionmentioning

confidence: 99%

Untitled

Sherstov¹

2013

Theory of Comput.

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“…However, this model assumes a complete communication network and single-bit transmissions. An extension of this line of work for random planar networks was also studied [26,38,12,13]. Unlike our own model, in this model a node can receive a message from multiple neighbors in a single round.…”

Section: Related Workmentioning

confidence: 94%

Broadcasting in Noisy Radio Networks

Censor-Hillel

Haeupler

Hershkowitz

et al. 2017

Proceedings of the ACM Symposium on Principles of Distributed Computing

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The widely-studied radio network model [Chlamtac and Kutten, 1985] is a graph-based description that captures the inherent impact of collisions in wireless communication. In this model, the strong assumption is made that node $v$ receives a message from a neighbor if and only if exactly one of its neighbors broadcasts. We relax this assumption by introducing a new noisy radio network model in which random faults occur at senders or receivers. Specifically, for a constant noise parameter $p \in [0,1)$, either every sender has probability $p$ of transmitting noise or every receiver of a single transmission in its neighborhood has probability $p$ of receiving noise. We first study single-message broadcast algorithms in noisy radio networks and show that the Decay algorithm [Bar-Yehuda et al., 1992] remains robust in the noisy model while the diameter-linear algorithm of Gasieniec et al., 2007 does not. We give a modified version of the algorithm of Gasieniec et al., 2007 that is robust to sender and receiver faults, and extend both this modified algorithm and the Decay algorithm to robust multi-message broadcast algorithms. We next investigate the extent to which (network) coding improves throughput in noisy radio networks. We address the previously perplexing result of Alon et al. 2014 that worst case coding throughput is no better than worst case routing throughput up to constants: we show that the worst case throughput performance of coding is, in fact, superior to that of routing -- by a $\Theta(\log(n))$ gap -- provided receiver faults are introduced. However, we show that any coding or routing scheme for the noiseless setting can be transformed to be robust to sender faults with only a constant throughput overhead. These transformations imply that the results of Alon et al., 2014 carry over to noisy radio networks with sender faults.Comment: Principles of Distributed Computing 201

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Lower Bounds for Noisy Wireless Networks using Sampling Algorithms

Cited by 8 publications

References 12 publications

How Hard is Computing Parity with Noisy Communications?

How Hard is Computing Parity with Noisy Communications?

Untitled

Broadcasting in Noisy Radio Networks

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