Wireless Broadcast with Short Labels

Bu, Gewu; Potop-Butucaru, Maria; Rabie, Mikaël

doi:10.1007/978-3-030-67087-0_10

“…In 2006, Fraigniaud, Ilcinkas, and Pelc [13] proposed measuring the amount of advice needed to solve various a distributed problems, and later Ilcinkas, Kowalski, and Pelc [14] applied this to the problem of broadcast in a radio network. Further results on this were given by Ellen, Gorain, Miller, and Pelc [11], Ellen and Gilbert [10], and Bu, Potop-Butucaru, and Rabie [4]. These results differed from our results on perfect advice in Section 3 in that they focused on multihop networks, giving a small number of distinct bits of advice to each node.…”

Section: Other Related Workmentioning

confidence: 53%

“…Implicit in this definition is the assumption that the network size is always of size at least 2 as there is no contention to resolve in a network of size less than 2. 4 The random variable ( ) takes its values from ( ). For each ∈ ( ), let = Pr ( ( ) = ), defined as follows:…”

Section: Preliminariesmentioning

confidence: 99%

Contention Resolution with Predictions

Gilbert

¹

,

Newport

²

,

Vaidya

³

et al. 2021

Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

View full text Add to dashboard Cite

In this paper, we consider contention resolution algorithms that are augmented with predictions about the network. We begin by studying the natural setup in which the algorithm is provided a distribution defined over the possible network sizes that predicts the likelihood of each size occurring. The goal is to leverage the predictive power of this distribution to improve on worst-case time complexity bounds. Using a novel connection between contention resolution and information theory, we prove lower bounds on the expected time complexity with respect to the Shannon entropy of the corresponding network size random variable, for both the collision detection and no collision detection assumptions. We then analyze upper bounds for these settings, assuming now that the distribution provided as input might differ from the actual distribution generating network sizes. We express their performance with respect to both entropy and the statistical divergence between the two distributions-allowing us to quantify the cost of poor predictions. Finally, we turn our attention to the related perfect advice setting, parameterized with a length ≥ 0, in which all active processes in a given execution are provided the best possible bits of information about their network. We provide tight bounds on the speed-up possible with respect to for deterministic and randomized algorithms, with and without collision detection. These bounds provide a fundamental limit on the maximum power that can be provided by any predictive model with a bounded output size.

show abstract

“…In 2006, Fraigniaud, Ilcinkas, and Pelc [12] proposed measuring the amount of advice needed to solve various a distributed problems, and later Ilcinkas, Kowalski, and Pelc [13] applied this to the problem of broadcast in a radio network. Further results on this were given by Ellen, Gorain, Miller, and Pelc [10], Ellen and Gilbert [9], and Bu, Potop-Butucaru, and Rabie [3]. These results differed from our results on perfect advice in Section 3 in that they focused on multihop networks, giving a small number of distinct bits of advice to each node.…”

Section: Other Related Workmentioning

confidence: 53%

“…We support this conjecture by noting a straightforward application of a cryptography result due to Pliam [19] indicates that for every constant ≥ 1, there is a random variable such that this strategy requires more than 2 ( ( )) rounds to succeed with constant probability. 3 An important characteristic of the Kullback-Leibler divergence is that is if each probability in is off by at most a bounded constant fraction from the real probability in ,…”

Section: Contention Resolution With Network Size Predictionsmentioning

confidence: 99%

See 1 more Smart Citation

Contention Resolution with Predictions

Gilbert¹,

Newport²,

Vaidya³

et al. 2021

Preprint

0

View full text Add to dashboard Cite

In this paper, we consider contention resolution algorithms that are augmented with predictions about the network. We begin by studying the natural setup in which the algorithm is provided a distribution defined over the possible network sizes that predicts the likelihood of each size occurring. The goal is to leverage the predictive power of this distribution to improve on worst-case time complexity bounds. Using a novel connection between contention resolution and information theory, we prove lower bounds on the expected time complexity with respect to the Shannon entropy of the corresponding network size random variable, for both the collision detection and no collision detection assumptions. We then analyze upper bounds for these settings, assuming now that the distribution provided as input might differ from the actual distribution generating network sizes. We express their performance with respect to both entropy and the statistical divergence between the two distributions-allowing us to quantify the cost of poor predictions. Finally, we turn our attention to the related perfect advice setting, parameterized with a length ≥ 0, in which all active processes in a given execution are provided the best possible bits of information about their network. We provide tight bounds on the speed-up possible with respect to for deterministic and randomized algorithms, with and without collision detection. These bounds provide a fundamental limit on the maximum power that can be provided by any predictive model with a bounded output size.

show abstract