Approximating the Size of a Radio Network in Beeping Model

Brandes, Philipp; Kardas, Marcin; Klonowski, Marek; Pająk, Dominik; Wattenhofer, Roger

doi:10.1007/978-3-319-48314-6_23

Cited by 13 publications

(7 citation statements)

References 21 publications

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“…The maximum allowed failure probability of a randomized algorithm is at most 1/poly(n). In a failed execution, devices may consume unbounded energy and never halt [29,30,8].…”

Section: Introductionmentioning

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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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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“…The maximum allowed failure probability of a randomized algorithm is at most 1/poly(n). In a failed execution, devices may consume unbounded energy and never halt [29,30,8].…”

Section: Introductionmentioning

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

View full text Add to dashboard Cite

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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: 60%

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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“…This procedure takes O(log log n + log f /ε 2 ) time slots. This result was also proved to be time-optimal in [4]. In [5] Chen, Zhou and Yu demonstrated a size approximation protocol for seemingly different model (namely RFID system) that needs Ω( 1 2 log 1/ + log log n) slots for ∈ [1/ √ n, 0.5] and negligible probability of failure.…”

Section: Related Workmentioning

confidence: 84%

Ordered and delayed adversaries and how to work against them on a shared channel

2018

Self Cite

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An execution of a distributed algorithm is often seen as a game between the algorithm and a conceptual adversary causing specific distractions to the computation. In this work we define a class of ordered adaptive adversaries, which cause distractions -in particular crashes -online according to some partial order of the participating stations, which is fixed by the adversary before the execution. We distinguish: Linearly-Ordered adversary, which is restricted by some pre-defined linear order of (potentially) crashing stations; Anti-Chain-Ordered adversary, previously known as the Weakly-Adaptive adversary, which is restricted by some pre-defined set of crash-prone stations (it can be seen as an ordered adversary with the order being an anti-chain, i.e., a collection of incomparable elements, consisting of these stations); k-Thick-Ordered adversary restricted by partial orders of stations with a maximum anti-chain of size k. We initiate a study of how they affect performance of algorithms. For this purpose, we focus on the well-known Do-All problem of performing t tasks by p synchronous crash-prone stations communicating on a shared channel. The channel restricts communication by the fact that no message is delivered to the operational stations if more than one station transmits at the same time. The question addressed in this work is how the ordered adversaries controlling crashes of stations influence work performance, defined as the total number of available processor steps during the whole execution and introduced by Kanellakis and Shvartsman in [26] in the context of Write-All algorithms. The first presented algorithm solves the Do-All problem with work O(t + p √ t log p) against the Linearly-Ordered adversary. Surprisingly, the upper bound on performance of this algorithm does not depend on the number of crashes f and is close to the absolute lower bound Ω(t + p √ t) proved in [11]. Another algorithm is developed against the Weakly-Adaptive adversary. Work done by this algorithm is O(t + p √ t + p min {p/(p − f ), t} log p), which is close to the lower bound Ω(t + p √ t + p min {p/(p − f ), t}) proved in [11] and answers the open questions posed there. We generalize this result to the class of k-Thick-Ordered adversaries, in which case the work of the algorithm is bounded by O(t + p √ t + p min {p/(p − f ), k, t} log p). We complement this result by proving the almost matching lower bound Ω(t + p √ t + p min {p/(p − f ), k, t}). Independently from the results for the ordered adversaries, we consider a class of delayed adaptive adversaries, which could see random choices with some delay. We present an algorithm that works efficiently against the 1-RD adversary, which could see random choices of stations with one round delay, achieving close to optimal O(t + p √ t log 2 p) work complexity. This shows that restricting the adversary by not allowing it to react on random decisions immediately makes it significantly weaker, in the sense that there is an algorithm achieving (almost) optimal work performance.

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Approximating the Size of a Radio Network in Beeping Model

Cited by 13 publications

References 21 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

Ordered and delayed adversaries and how to work against them on a shared channel

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