Reductions in Distributed Computing Part II: k-Threshold Agreement Tasks

Details Reductions in Distributed Computing Part II: k-Threshold Agreement Tasks Reductions in Distributed Computing Part II: k-Threshold Agreement Tasks

2004-12-29

arxiv.org/abs/cs/0412116v1

Computer Science

Distributed, Parallel, and Cluster Computing

27 pages, 4 figures

Scientific paper

We extend the results of Part I by considering a new class of agreement tasks, the so-called k-Threshold Agreement tasks (previously introduced by Charron-Bost and Le Fessant). These tasks naturally interpolate between Atomic Commitment and Consensus. Moreover, they constitute a valuable tool to derive irreducibility results between Consensus tasks only. In particular, they allow us to show that (A) for a fixed set of processes, the higher the resiliency degree is, the harder the Consensus task is, and (B) for a fixed resiliency degree, the smaller the set of processes is, the harder the Consensus task is. The proofs of these results lead us to consider new oracle-based reductions, involving a weaker variant of the C-reduction introduced in Part I. We also discuss the relationship between our results and previous ones relating f-resiliency and wait-freedom.

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