Probabilistic Algorithms for the Wakeup Problem in Single-Hop Radio Networks

Jurdziński, Tomasz; Stachowiak, Grzegorz

doi:10.1007/3-540-36136-7_47

Cited by 86 publications

(91 citation statements)

References 14 publications

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“…They differ in some aspects of the model, such as whether the nodes can detect collision or cannot distinguish between a collision and silence, and whether the nodes know the entire network graph, or know only their neighbors, or do not have any such knowledge at all. Some papers that studied local broadcast are [11,27], where deterministic algorithms were presented, and [6,21,33], which studied randomized algorithms.…”

Section: Related Workmentioning

confidence: 99%

Bounded-Contention Coding for the additive network model

Censor-Hillel

Haeupler²,

Lynch³

et al. 2015

Distrib. Comput.

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Efficient communication in wireless networks is typically challenged by the possibility of interference among several transmitting nodes. Much important research has been invested in decreasing the number of collisions in order to obtain faster algorithms for communication in such networks.This paper proposes a novel approach for wireless communication, which embraces collisions rather than avoiding them, over an additive channel. It introduces a coding technique called Bounded-Contention Coding (BCC) that allows collisions to be successfully decoded by the receiving nodes into the original transmissions and whose complexity depends on a bound on the contention among the transmitters.BCC enables deterministic local broadcast in a network with n nodes and at most a transmitters with information of bits each within O(a log n + a ) bits of communication with full-duplex radios, and O((a log n + a )(log n)) bits, with high probability, with half-duplex radios. When combined with random linear network coding, BCC gives global broadcast within O((D + a + log n)(a log n + )) bits, with high probability. This also holds in dynamic networks that can change arbitrarily over time by a worst-case adversary. When no bound on the contention is given, it is shown how to probabilistically estimate it and obtain global broadcast that is adaptive to the true contention in the network.

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Section: Related Workmentioning

confidence: 99%

Bounded-Contention Coding for the additive network model

Censor-Hillel

Haeupler²,

Lynch³

et al. 2015

Distrib. Comput.

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“…To put this result in context, in the single channel model, building an MIS requires Θ(log 2 n) time [11,18,20,24]. Based on the lower bound techniques developed in [10,11,13,20], we show in [9] that in bounded independence graphs (and even in unit-disk graphs) any MIS algorithm requires at least Ω log 2 n F + log n rounds in a network with F channels.…”

Section: Introductionmentioning

confidence: 94%

“…Based on the lower bound techniques developed in [10,11,13,20], we show in [9] that in bounded independence graphs (and even in unit-disk graphs) any MIS algorithm requires at least Ω log 2 n F + log n rounds in a network with F channels. Our algorithm matches this multichannel lower bound up to poly(log log n) factors and beats the single channel lower bound.…”

Section: Introductionmentioning

confidence: 99%

Maximal independent sets in multichannel radio networks

Daum

Ghaffari

Gilbert

et al. 2013

Proceedings of the 2013 ACM Symposium on Principles of Distributed Computing

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We present new upper bounds for fundamental problems in multichannel wireless networks. These bounds address the benefits of dynamic spectrum access, i.e., to what extent multiple communication channels can be used to improve performance. In more detail, we study a multichannel generalization of the standard graph-based wireless model without collision detection, and assume the network topology satisfies polynomially bounded independence.Our core technical result is an algorithm that constructs a maximal independent set (MIS) in O log 2 n F +Õ(log n) rounds, in networks of size n with F channels, where thẽ O-notation hides polynomial factors in log log n.Moreover, we use this MIS algorithm as a subroutine to build a constant-degree connected dominating set in the same asymptotic time. Leveraging this structure, we are able to solve global broadcast and leader election within O D + log 2 n F +Õ(log n) rounds, where D is the diameter of the graph, and k-message multi-message broadcast in O D +k + log 2 n F +Õ(log n) rounds for unrestricted message size (with a slow down of only a log factor on the k term under the assumption of restricted message size).In all five cases above, we prove: (a) our results hold with high probability (i.e., at least 1 − 1/n); (b) our results are within poly(log log n)-factors of the relevant lower bounds for multichannel networks; and (c) our results beat the relevant lower bounds for single channel networks. These new (near) optimal algorithms significantly expand the number of problems now known to be solvable faster in multichannel versus single channel wireless networks.

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“…In beeping, radio or sensor network models, degree information is not generally provided. For the maximal independent set problem, algorithms with degree information generally outperform algorithms that operate without such information: While for many models that do not provide degree information, algorithms typically use Ω(log 2 n) rounds [1,10,19,20,29,30] (see also the Ω(log 2 / log log n) lower bound of [21]), degree information as employed for example in Luby's algorithm [2,28] allows for O(log n) rounds. In our one-round setting, degree information is however crucial for obtaining non-trivial approximation guarantees.…”

Section: Model Requirementsmentioning

confidence: 99%

Computing large independent sets in a single round

Halldórsson

Konrad

2017

Distrib. Comput.

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Independent sets play a central role in distributed algorithmics. We examine here the minimal requirements for computing non-trivial independent sets. In particular, we focus on algorithms that operate in a single communication round. A classic result of Linial shows that a constant number of rounds does not suffice to compute a maximal independent set. We are therefore interested in the size of the solution that can be computed, especially in comparison to the optimal. Our main result is a randomized one-round algorithm that achieves poly-logarithmic approximation on graphs of polynomially bounded-independence. Specifically, we show that the algorithm achieves the Caro-Wei bound (an extension of the Turán bound for independent sets) in general graphs up to a constant factor, and that the Caro-Wei bound yields a poly-logarithmic approximation on bounded-independence graphs. The algorithm uses only a single bit message and operates in a beeping model, where a node receives only the disjunction of the bits transmitted by its neighbors. We give limitation results that show that these are the minimal requirements for obtaining non-trivial solutions. In particular, a sublinear approximation cannot be obtained in a single round on general graphs, nor when nodes cannot both transmit and receive messages. We also show that our analysis of the Caro-Wei bound on polynomially bounded-independence graphs is tight, and that the poly-logarithmic approximation factor does not extend to O(1)-claw free graphs.

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Probabilistic Algorithms for the Wakeup Problem in Single-Hop Radio Networks

Cited by 86 publications

References 14 publications

Bounded-Contention Coding for the additive network model

Bounded-Contention Coding for the additive network model

Maximal independent sets in multichannel radio networks

Computing large independent sets in a single round

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