On the radius of nonsplit graphs and information dissemination in dynamic networks

Függer, Matthias; Nowak, Thomas; Winkler, Kyrill

doi:10.1016/j.dam.2020.02.013

Cited by 4 publications

(7 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There has also been interest in a problem variant which only differs in the pool of networks the adversary can choose a network from for each communication round. Függer, Nowak, and Winkler [9] give an O(log log n) upper bound if the adversary can only choose nonsplit graphs. Combined with the result of Charron-Bost, Függer, and Nowak [1] that states that one can simulate n − 1 rounds of rooted trees with a round of a nonsplit graph, this gives the previous O(n log log n) upper bound for our problem.…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

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

View full text Add to dashboard Cite

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.

show abstract

Section: Related Workmentioning

confidence: 99%

“…− 2 lower bound. 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.…”

Section: Introductionmentioning

confidence: 99%

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

View full text Add to dashboard Cite

show abstract

“…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: 72%

“…Our results also shed an interesting new light on the relationship between distributed consensus and broadcast: as the input value of some process is known to reach all other processes in almost linear time under any oblivious message adversary [16], one might be tempted to expect that consensus solvability can also be decided fast. Our results show that, quite on the contrary, reaching consensus can take exponential time.…”

Section: Our Contributionsmentioning

confidence: 88%

Time Complexity of Consensus in Dynamic Networks Under Oblivious Message Adversaries

Paz¹,

Galeana²,

Schmid³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…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%

Time Complexity of Broadcast and Consensus for Randomized Oblivious Message Adversaries

El-Hayek¹,

Henzinger²,

Schmid³

2023

Preprint

View full text Add to dashboard Cite

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.

show abstract

On the radius of nonsplit graphs and information dissemination in dynamic networks

Cited by 4 publications

References 15 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

Time Complexity of Broadcast and Consensus for Randomized Oblivious Message Adversaries

Contact Info

Product

Resources

About