Abstract
Shared data structures are a basic building block in distributed computing, but can be expensive to implement. One way to circumvent the high implementation cost of linearizability is to relax the sequential specification of the data type. This gives up some guarantees, for instance on the ordering of data elements, as a tradeoff against performance. We want to explore the effects of this tradeoff on the computational power of the shared data structures. In this paper, we characterize the effects of three different types of relaxation, chosen from the literature, on the computational power of FIFO queues. By parametrically relaxing each of the three operations on a queue (Enqueue, Dequeue, Peek), we obtain an infinite 3-dimensional space for each type of relaxation. We find the consensus number, a standard measure of the computational power of shared data types, of each point in these spaces, completely describing the effect of these three types of relaxation on the computational power of queues.
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Notes
This is a standard assumption and is used to clarify definitions and discussions of double-Dequeues and similar errors. It can be assumed WLOG because we have not restricted the type of the queues we consider. We can thus, when implementing a queue to hold a desired type T, instead implement one holding the pair (T,tag), putting a unique tag (such as a process id and local sequence counter) as the second element of each pair.
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Acknowledgements
This work was supported in part by NSF Grant 1526725. We would like to thank the anonymous reviewers for their helpful comments which improved the paper’s presentation.
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Talmage, E., Welch, J.L. Anomalies and similarities among consensus numbers of variously-relaxed queues. Computing 101, 1349–1368 (2019). https://doi.org/10.1007/s00607-018-0661-2
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DOI: https://doi.org/10.1007/s00607-018-0661-2