Time Complexity of Broadcast and Consensus for Randomized Oblivious Message Adversaries

by   Antoine El-Hayek, et al.

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.


page 1

page 2

page 3

page 4


Time Complexity of Consensus in Dynamic Networks Under Oblivious Message Adversaries

Consensus is a most fundamental task in distributed computing. This pape...

Breaking the (√(n)) Barrier: Fast Consensus under a Late Adversary

We study the consensus problem in a synchronous distributed system of n ...

The Communication Cost of Information Spreading in Dynamic Networks

This paper investigates the message complexity of distributed informatio...

Robustness of Randomized Rumour Spreading

In this work we consider three well-studied broadcast protocols: Push, P...

Smoothed Analysis of Information Spreading in Dynamic Networks

The best known solutions for k-message broadcast in dynamic networks of ...

Improved Communication Complexity of Fault-Tolerant Consensus

Consensus is one of the most thoroughly studied problems in distributed ...

Efficient Computation in Congested Anonymous Dynamic Networks

An "anonymous dynamic network" is a network of indistinguishable process...

Please sign up or login with your details

Forgot password? Click here to reset