Gossiping in a multi-channel radio network an oblivious approach to coping with malicious interference

• Authors: Shlomi Dolev;Seth Gilbert;Rachid Guerraoui;Calvin Newport
• Venue: DISC'07 Proceedings of the 21st international conference on Distributed Computing
• Year: 2007

We study oblivious deterministic gossip algorithms for multi-channel radio networks with a malicious adversary. In a multi-channel network, each of the n processes in the system must choose, in each round, one of the c channels of the system on which to participate. Assuming the adversary can disrupt one channel per round, preventing communication on that channel, we establish a tight bound of max (Θ-((1-ε)n/c-1 + log cn), Θ (n(1-ε)/εc2)) on the number of rounds needed to solve the ε-gossip problem, a parameterized generalization of the all-to-all gossip problem that requires (1-ε)n of the "rumors" to be successfully disseminated. Underlying our lower bound proof lies an interesting connection between ε-gossip and extremal graph theory. Specifically, we make use of Turán's theorem, a seminal result in extremal combinatorics, to reason about an adversary's optimal strategy for disrupting an algorithm of a given duration. We then show how to generalize our upper bound to cope with an adversary that can simultaneously disrupt t c channels. Our generalization makes use of selectors: a combinatorial tool that guarantees that any subset of processes will be "selected" by some set in the selector. We prove this generalized algorithm optimal if a maximum number of values is to be gossiped. We conclude by extending our algorithm to tolerate traditional Byzantine corruption faults.