TY - GEN

T1 - Gossiping in a multi-channel radio network an oblivious approach to coping with malicious interference

AU - Dolev, Shlomi

AU - Gilbert, Seth

AU - Guerraoui, Rachid

AU - Newport, Calvin

PY - 2007/1/1

Y1 - 2007/1/1

N2 - 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 (⊖ ((1-ε)n/c-1 + logc n), ⊖ (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.

AB - 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 (⊖ ((1-ε)n/c-1 + logc n), ⊖ (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.

UR - http://www.scopus.com/inward/record.url?scp=38049032492&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-75142-7_18

DO - 10.1007/978-3-540-75142-7_18

M3 - Conference contribution

AN - SCOPUS:38049032492

SN - 9783540751410

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 208

EP - 222

BT - Distributed Computing - 21st International Symposium, DISC 2007, Proceedings

PB - Springer Verlag

T2 - 21st International Symposium on Distributed Computing, DISC 2007

Y2 - 24 September 2007 through 26 September 2007

ER -