The Weakest Failure Detector for Genuine Atomic Multicast

Atomic broadcast is a group communication primitive to order messages across a set of distributed processes. Atomic multicast is its natural generalization where each message m is addressed to dst(m), a subset of the processes called its destination group. A solution to atomic multicast is genuine when a process takes steps only if a message is addressed to it. Genuine solutions are the ones used in practice because they have better performance. Let G be all the destination groups and F be the cyclic families in it, that is the subsets of G whose intersection graph is hamiltonian. This paper establishes that the weakest failure detector to solve genuine atomic multicast is µ = (∧_g,h∈G Σ_g∩h) ∧ (∧_g∈G Ω_g) ∧ γ, where Σ_P and Ω_P are the quorum and leader failure detectors restricted to the processes in P, and γ is a new failure detector that informs the processes in a cyclic family f ∈ F when f is faulty. We also study two classical variations of atomic multicast. The first variation requires that message delivery follows the real-time order. In this case, µ must be strengthened with 1^g∩h, the indicator failure detector that informs each process in g∪h when g∩h is faulty. The second variation requires a message to be delivered when the destination group runs in isolation. We prove that its weakest failure detector is at least µ ∧ (∧_g,h∈G Ω_g∩h). This value is attained when F = ∅.