Brief Announcement: Broadcasting Time in Dynamic Rooted Trees is Linear

El-Hayek, Antoine; Henzinger, Monika; Schmid, Stefan

doi:10.1145/3519270.3538460

Cited by 2 publications

(6 citation statements)

References 17 publications

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“…Note that in the case k = n − 1, this is the deterministic case where in each round the adversary gets to exactly choose which tree is the communication network of the round. This is exactly the model studied in [13], where it was shown that the adversary cannot delay broadcast for more than (1 + √ 2)n ≈ 2.4n.…”

Section: The Randomized Oblivious Message Adversarysupporting

confidence: 54%

“…Dobrev and Vrto [9,8] give specific results when the adversary is restricted to hypercubic and tori graphs with some missing edges. El-Hayek, Henzinger, and Schmid [12,13] recently settled the question about the asymptotic time complexity of broadcast by giving a tight O(n) upper bound, also showing the upper bound still holds in more general models. Regarding consensus, Coulouma, Godard and Peters in [6] presented a general characterization on which dynamic graphs consensus is solvable, based on broadcastability.…”

Section: Related Workmentioning

confidence: 99%

“…In this section, we consider a very similar model to [13], the only difference being that the adversary is restricted to choosing trees of height at most 2.…”

Section: A Lower Bound For Deterministic Broadcast In Constant Height...mentioning

confidence: 99%

“…The question is: how many rounds can the adversary delay broadcast, depending on A? Authors in [13] have shown that if A is the set of rooted trees, then the adversary can delay broadcast for a linear number of rounds. Since a linear number of rounds is easily achievable by the adversary simply by taking a line graph L, and using L as the communication network in each round, one would think that the height of the trees allowed play an important role to determine broadcast time.…”

Section: A Lower Bound For Deterministic Broadcast In Constant Height...mentioning

confidence: 99%

“…In our second model an adversary can influence the network that is chosen in each round. The setting where the adversary completely determines the tree was studied in [28,17] and Broadcast in that model was recently solved: The required number of rounds is Θ(n) [17,13], while Consensus is unsolvable [6]. We generalize this model and consider the Randomized Oblivious Message Adversary model, where the power of the adversary is controlled by a parameter k. In that model, to construct the communication network for a round, the adversary chooses k directed edges to appear in the tree, and a rooted tree is chosen uniformly at random among the trees from T n that include those k edges.…”

Section: Introductionmentioning

confidence: 99%

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Time Complexity of Broadcast and Consensus for Randomized Oblivious Message Adversaries

El-Hayek¹,

Henzinger²,

Schmid³

2023

Preprint

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Broadcast and consensus are most fundamental tasks in distributed computing. These tasks are particularly challenging in dynamic networks where communication across the network links may be unreliable, e.g., due to mobility or failures. Indeed, over the last years, researchers have derived several impossibility results and high time complexity lower bounds (i.e., linear in the number of nodes n) for these tasks, even for oblivious message adversaries where communication networks are rooted trees. However, such deterministic adversarial models may be overly conservative, as many processes in real-world settings are stochastic in nature rather than worst case.This paper initiates the study of broadcast and consensus on stochastic dynamic networks, introducing a randomized oblivious message adversary. Our model is reminiscent of the SI model in epidemics, however, revolving around trees (which renders the analysis harder due to the apparent lack of independence). In particular, we show that if information dissemination occurs along random rooted trees, broadcast and consensus complete fast with high probability, namely in logarithmic time. Our analysis proves the independence of a key variable, which enables a formal understanding of the dissemination process.More formally, for a network with n nodes, we first consider the completely random case where in each round the communication network is chosen uniformly at random among rooted trees. We then introduce the notion of randomized oblivious message adversary, where in each round, an adversary can choose k edges to appear in the communication network, and then a rooted tree is chosen uniformly at random among the set of all rooted trees that include these edges. We show that broadcast completes in O(k + log n) rounds, and that this it is also the case for consensus as long as k ≤ 0.1n.

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Section: The Randomized Oblivious Message Adversarysupporting

confidence: 54%

Section: Related Workmentioning

confidence: 99%

“…In this section, we consider a very similar model to [13], the only difference being that the adversary is restricted to choosing trees of height at most 2.…”

Section: A Lower Bound For Deterministic Broadcast In Constant Height...mentioning

confidence: 99%

Section: A Lower Bound For Deterministic Broadcast In Constant Height...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Time Complexity of Broadcast and Consensus for Randomized Oblivious Message Adversaries

El-Hayek¹,

Henzinger²,

Schmid³

2023

Preprint

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The Time Complexity of Consensus Under Oblivious Message Adversaries

Winkler,

Paz,

Galeana

et al. 2024

Algorithmica

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We study the problem of solving consensus in synchronous directed dynamic networks, in which communication is controlled by an oblivious message adversary that picks the communication graph to be used in a round from a fixed set of graphs $$\textbf{D}$$ D arbitrarily. In this fundamental model, determining consensus solvability and designing efficient consensus algorithms is surprisingly difficult. Enabled by a decision procedure that is derived from a well-established previous consensus solvability characterization for a given set $$\textbf{D}$$ D , we study, for the first time, the time complexity of solving consensus in this model: We provide both upper and lower bounds for this time complexity, and also relate it to the number of iterations required by the decision procedure. Among other results, we find that reaching consensus under an oblivious message adversary can take exponentially longer than both deciding consensus solvability and broadcasting the input value of some unknown process to all other processes.

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Brief Announcement: Broadcasting Time in Dynamic Rooted Trees is Linear

Cited by 2 publications

References 17 publications

Time Complexity of Broadcast and Consensus for Randomized Oblivious Message Adversaries

Time Complexity of Broadcast and Consensus for Randomized Oblivious Message Adversaries

The Time Complexity of Consensus Under Oblivious Message Adversaries

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