4 research outputs found
Optimal Gossip with Direct Addressing
Gossip algorithms spread information by having nodes repeatedly forward
information to a few random contacts. By their very nature, gossip algorithms
tend to be distributed and fault tolerant. If done right, they can also be fast
and message-efficient. A common model for gossip communication is the random
phone call model, in which in each synchronous round each node can PUSH or PULL
information to or from a random other node. For example, Karp et al. [FOCS
2000] gave algorithms in this model that spread a message to all nodes in
rounds while sending only messages per node
on average.
Recently, Avin and Els\"asser [DISC 2013], studied the random phone call
model with the natural and commonly used assumption of direct addressing.
Direct addressing allows nodes to directly contact nodes whose ID (e.g., IP
address) was learned before. They show that in this setting, one can "break the
barrier" and achieve a gossip algorithm running in
rounds, albeit while using messages per node.
We study the same model and give a simple gossip algorithm which spreads a
message in only rounds. We also prove a matching lower bound which shows that this running time is best possible. In
particular we show that any gossip algorithm takes with high probability at
least rounds to terminate. Lastly, our algorithm can be
tweaked to send only messages per node on average with only
bits per message. Our algorithm therefore simultaneously achieves the optimal
round-, message-, and bit-complexity for this setting. As all prior gossip
algorithms, our algorithm is also robust against failures. In particular, if in
the beginning an oblivious adversary fails any nodes our algorithm still,
with high probability, informs all but surviving nodes
Consensus Needs Broadcast in Noiseless Models but can be Exponentially Easier in the Presence of Noise
Consensus and Broadcast are two fundamental problems in distributed computing, whose solutions have several applications. Intuitively, Consensus should be no harder than Broadcast, and this can be rigorously established in several models. Can Consensus be easier than Broadcast? In models that allow noiseless communication, we prove a reduction of (a suitable variant of) Broadcast to binary Consensus, that preserves the communication model and all complexity parameters such as randomness, number of rounds, communication per round, etc., while there is a loss in the success probability of the protocol. Using this reduction, we get, among other applications, the first logarithmic lower bound on the number of rounds needed to achieve Consensus in the uniform GOSSIP model on the complete graph. The lower bound is tight and, in this model, Consensus and Broadcast are equivalent. We then turn to distributed models with noisy communication channels that have been studied in the context of some bio-inspired systems. In such models, only one noisy bit is exchanged when a communication channel is established between two nodes, and so one cannot easily simulate a noiseless protocol by using error-correcting codes. An lower bound on the number of rounds needed for Broadcast is proved by Boczkowski et al. [PLOS Comp. Bio. 2018] in one such model (noisy uniform PULL, where is a parameter that measures the amount of noise). In such model, we prove a new bound for Broadcast and a bound for binary Consensus, thus establishing an exponential gap between the number of rounds necessary for Consensus versus Broadcast