The Computational Power of Beeps

Gilbert, Seth; Newport, Calvin

doi:10.1007/978-3-662-48653-5_3

Cited by 19 publications

(23 citation statements)

References 22 publications

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“…Cornejo and Kuhn [13] introduced the beeping model, where no messages are sent; the only signals are λ N and λ S : noise and silence. The complexity of Approximate Counting was studied in [8] and the "state complexity" of Leader Election was studied in [26].In adversarial settings a jammer can interfere with communication. See [39,17] for leader election protocols resilient to jamming.…”

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confidence: 99%

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Exponential separations in the energy complexity of leader election

Chang

Kopelowitz

Pettie

et al. 2017

Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing

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Energy is often the most constrained resource for battery-powered wireless devices and the lion's share of energy is often spent on transceiver usage (sending/receiving packets), not on computation. In this paper we study the energy complexity of Leader Election and Approximate Counting in several models of wireless radio networks. It turns out that energy complexity is very sensitive to whether the devices can generate random bits and their ability to detect collisions. We consider four collision-detection models: Strong-CD (in which transmitters and listeners detect collisions), Sender-CD and Receiver-CD (in which only transmitters or only listeners detect collisions), and No-CD (in which no one detects collisions.)The take-away message of our results is quite surprising. For randomized Leader Election algorithms, there is an exponential gap between the energy complexity of Sender-CD and Receiver-CD:Randomized: No-CD = Sender-CD Receiver-CD = Strong-CD and for deterministic Leader Election algorithms, there is another exponential gap in energy complexity, but in the reverse direction:In particular, the randomized energy complexity of Leader Election is Θ(log * n) in Sender-CD but Θ(log(log * n)) in Receiver-CD, where n is the (unknown) number of devices. Its deterministic complexity is Θ(log N ) in Receiver-CD but Θ(log log N ) in Sender-CD, where N is the (known) size of the devices' ID space.There is a tradeoff between time and energy. We give a new upper bound on the time-energy tradeoff curve for randomized Leader Election and Approximate Counting. A critical component of this algorithm is a new deterministic Leader Election algorithm for dense instances, when n = Θ(N ), with inverse-Ackermann-type (O(α(N ))) energy complexity.

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confidence: 99%

Exponential separations in the energy complexity of leader election

Chang

Kopelowitz

Pettie

et al. 2017

Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing

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“…This aligns with the beeping model introduced by Cornejo and Kuhn [34]. Under this model, both leader election [42] and counting [24,21] have been investigated.…”

Section: Related Workmentioning

confidence: 57%

Contention Resolution with Constant Throughput and Log-Logstar Channel Accesses

Bender¹,

Kopelowitz²,

Pettie³

et al. 2018

SIAM J. Comput.

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For decades, randomized exponential backoff has provided a critical algorithmic building block in situations where multiple devices seek access to a shared resource. Despite this history, the performance of standard exponential backoff is poor under worst-case scheduling of demands on the resource: (i) subconstant throughput can occur under plausible scenarios, and (ii) each of N devices requires Ω(log N ) access attempts before obtaining the resource. In this paper, we address these shortcomings by offering a new backoff protocol for a shared communication channel that guarantees expected constant throughput with only O(log(log * N )) channel accesses in expectation, even when packet arrivals are scheduled by an adversary. Central to this result are new algorithms for approximate counting and leader election with the same performance guarantees. ).1 Although it is usually fine to conflate the players with their associated packets, we find it useful to distinguish them. For example, in our protocols, players are obliged to do more than merely guarantee that their packet is sent.2 The notation log indicates the logarithm base 2.

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“…Hence, when a problem is solved in some strong model, one naturally strives to solve it in a weaker model. In a recent series of works [7,19,1,10,20,9], the community has started to explore new models of communications that are even weaker than constant size messages in anonymous networks, namely beeping models.…”

Section: Introductionmentioning

confidence: 99%

Counting in one-hop beeping networks

Casteigts

Métivier

Robson

et al. 2019

Theoretical Computer Science

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We consider networks of processes which interact with beeps. In the basic model defined by Cornejo and Kuhn [7], which we refer to as the BL variant, processes can choose in each round either to beep or to listen. Those who beep are unable to detect simultaneous beeps. Those who listen can only distinguish between silence and the presence of at least one beep. Beeping models are weak in essence and even simple tasks may become difficult or unfeasible with them. In this paper, we address the problem of computing how many participants there are in a one-hop network: the counting problem. We first observe that no algorithm can compute this number with certainty in BL, whether the algorithm be deterministic or even randomised (Las Vegas). We thus consider the stronger variant where beeping nodes are able to detect simultaneous beeps, referred to as B cd L (for collision detection). We prove that at least n rounds are necessary in B cd L, and we present an algorithm whose running time is O(n) rounds with high probability. Further experimental results show that its expected running time is less than 10n. Finally, we discuss how this algorithm can be adapted in other beeping models. In particular, we show that it can be emulated in BL, at the cost of a logarithmic slowdown and of trading its Las Vegas nature (result certain, time uncertain) against Monte Carlo (time certain, result uncertain).

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The Computational Power of Beeps

Cited by 19 publications

References 22 publications

Exponential separations in the energy complexity of leader election

Exponential separations in the energy complexity of leader election

Contention Resolution with Constant Throughput and Log-Logstar Channel Accesses

Counting in one-hop beeping networks

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