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Each server will allocate pids monotonically so if PID N is expired then so is PID M for M > N. This means we can just keep a simple array/list of pid-entries, new entries are added to one end and expired from the other and lookup is just based on binary search. Servers will maintain a fixed amount of memory for pids by making the pid array of fixed size and use it as a circular buffer.

Both leader and followers will maintain this structure. They will periodically snapshot it to disk along with the current offset vector for all partitions they maintain. In the event of a crash they will use this snapshot and offsets to restore from the logs.

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Note that the expiration is only approximate as it is based on the time a server sees the first message for a partition. However it is only required that the server guarantee at least that much time, so retaining pids longer is okay. This means the followers can use arrival time (though arrival on followers will be slightly older than on the leader). In the event of a full data restore the circular buffer of pid entries will be full and all will have full expiration time restored.