Improved and Partially-Tight Lower Bounds for Message-Passing Implementations of Multiplicity Queues

A multiplicity queue is a concurrently-defined data type which relaxes the conditions of a linearizable FIFO queue to allow concurrent Dequeue instances to return the same value. It would seem that this should allow faster message-passing implementations, as processes should not need to wait as long to learn about concurrent operations at remote processes and previous work has shown that multiplicity queues are computationally less complex than the unrelaxed version. Intriguingly, other work has shown that there is, in fact, not much speedup possible versus an unrelaxed queue implementation. Seeking to understand this difference between intuition and real behavior, we improve the existing lower bound for uniform algorithms. We also give an upper bound for a special case to show that our bound is tight at that point. To achieve our lower bounds, we use extended shifting arguments, which are rarely used. We use these techniques in series of inductive indistinguishability proofs, extending our proofs beyond the usual limitations of traditional shifting arguments. This proof structure is an interesting contribution independently of the main result, as new lower bound proof techniques may have many uses in future work.