In discussion with sjlee0, vrushalic, subru, and curino a use-case came up to be able to map from application-id to cluster-id in context of federation for Yarn.
What happens is that a "random" cluster in the federation is asked to generate an app-id and then potentially a different cluster can be the "home" cluster for the AM. Furthermore, tasks can then run in yet other clusters.
In order to be able to pull up the logical home cluster on which the application ran, there needs to be a mapping from application-id to cluster-id. This mapping is available in the federated Yarn case only during the active live of the application.
A similar situation is common in our larger production environment. Somebody will complain about a slow job, some failure or whatever. If we're lucky we have an application-id. When we ask the user which cluster they ran on, they'll typically answer with the machine from where they launched the job (many users are unaware of the underlying physical clusters). This leaves us to spelunk through various RM ui's to find a matching epoch in the application ID.