On linear-time data dissemination in dynamic rooted trees

Zeiner, Martin; Schwarz, Manfred; Schmid, Ulrich

doi:10.1016/j.dam.2018.08.015

Cited by 6 publications

(10 citation statements)

References 35 publications

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“…We settle the open problem about time complexity of broadcast in dynamic networks, by showing that it is linear. Hence, Zeiner et al's [14] conjecture is true. In particular, we present an upper bound of (1 + √ 2)n − 1 .…”

Section: Contributionmentioning

confidence: 90%

“…In particular, we present an upper bound of (1 + √ 2)n − 1 . Combined with the lower bound given by [14], this yields the following theorem: Theorem 3.1. The broadcasting time in dynamic rooted trees is linear:…”

Section: Contributionmentioning

confidence: 91%

“…Results from Charron-Bost and Schiper in 2009 [2] and Charron-Bost, Függer, and Nowak in 2015 [1] imply an n log n upper bound. In 2019, Zeiner, Schwarz, and Schmid [14] gave a linear upper bound when the adversary is restricted to trees with either a constant number of leaves or a constant number of inner nodes. They also gave a 3n−1 2…”

Section: Introductionmentioning

confidence: 99%

“…In 2020, Függer, Nowak, and Winkler [9] improved the general upper bound to 2n log log n + O(n). So far, it has been an open conjecture [14] whether the broadcast time is linear for arbitrary sequences of rooted trees. We consider the following broadcasting problem.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Brief Announcement: Broadcasting Time in Dynamic Rooted Trees is Linear

El-Hayek

Henzinger

Schmid

2022

Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing

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We study the broadcast problem on dynamic networks with n processes. The processes communicate in synchronous rounds along an arbitrary rooted tree. The sequence of trees is given by an adversary whose goal is to maximize the number of rounds until at least one process reaches all other processes. Previous research has shown a 3n−1 2 − 2 lower bound and an O(n log log n) upper bound. We show the first linear upper bound for this problem, namely (1 + √ 2)n − 1 ≈ 2.4n. Our result follows from a detailed analysis of the evolution of the adjacency matrix of the network over time.

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Section: Contributionmentioning

confidence: 90%

Section: Contributionmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Brief Announcement: Broadcasting Time in Dynamic Rooted Trees is Linear

El-Hayek

Henzinger

Schmid

2022

Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing

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“…Our work hence complements previous work, which either primarily focuses on the feasibility of consensus [12] or the simpler broadcast problem [16,35]: how long it takes until the input value of some process has reached every other process.…”

mentioning

confidence: 74%

Time Complexity of Consensus in Dynamic Networks Under Oblivious Message Adversaries

Paz¹,

Galeana²,

Schmid³

et al. 2022

Preprint

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Consensus is a most fundamental task in distributed computing. This paper studies the consensus problem for a set of processes connected by a dynamic directed network, in which computation and communication is lock-step synchronous but controlled by an oblivious message adversary. In this basic model, determining consensus solvability and designing consensus algorithms in the case where it is possible, has been shown to be surprisingly difficult. We present an explicit decision procedure to determine if consensus is possible under a given adversary. This in turn enables us, for the first time, to study the time complexity of consensus in this model. In particular, we derive time complexity upper bounds for consensus solvability both for a centralized decision procedure as well as for solving distributed consensus. We complement these results with time complexity lower bounds. Intriguingly, we find that reaching consensus under an oblivious message adversary can take exponentially longer than broadcasting the input value of some process to all other processes.

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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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On linear-time data dissemination in dynamic rooted trees

Cited by 6 publications

References 35 publications

Brief Announcement: Broadcasting Time in Dynamic Rooted Trees is Linear

Brief Announcement: Broadcasting Time in Dynamic Rooted Trees is Linear

Time Complexity of Consensus in Dynamic Networks Under Oblivious Message Adversaries

The Time Complexity of Consensus Under Oblivious Message Adversaries

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