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

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... cyclic families in them, that is the groups whose intersection graph forms a cycle graph. This paper establishes that the weakest failure detector to solve genuine atomic multicast is 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 = ∅. CCS CONCEPTS • Theory of computation → Distributed computing models; • Software and its engineering → Distributed systems organizing principles; • General and reference → Reliability.