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The computability of relaxed data structures: queues and stacks as examples

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Abstract

Most concurrent data structures being designed today are versions of known sequential data structures. However, in various cases it makes sense to relax the semantics of traditional concurrent data structures in order to get simpler and possibly more efficient and scalable implementations. For example, when solving the classical producer-consumer problem by implementing a concurrent queue, it might be enough to allow the dequeue operation (by a consumer) to return and remove one of the two oldest values in the queue, and not necessarily the oldest one. We define infinitely many possible relaxations of several traditional data structures and objects: queues, stacks, multisets and registers, and examine their relative computational power.

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Notes

  1. The enqueue operation inserts a value to the queue and the dequeue operation returns and removes the oldest value in the queue. That is, the values are dequeued in the order in which they were enqueued. The peek operation reads the oldest value in the queue without removing it. If the queue is empty the dequeue and the peek operations return a special symbol.

  2. A position of an item in a queue or in a stack is simply the number of items which precede it plus one.

  3. To our surprise, we could not find any publication in which it is claimed that \(CN(stack[1,1,1]) = 2\). Nevertheless, we consider it as a known result.

  4. This is false, if the queue initially contains one element. In such a case, two processes can solve consensus, by deciding on the input of the process that successfully dequeues the element.

  5. Notice that we reach a contradiction, by assuming that p’s peek operation returns the first element in both passes. Since this implies that it cannot be the case that both events by p and q are peek events, there is no need to consider the sub-case where p’s peek operation returns the first element in one path and the second element is the other path.

  6. The known constructions of a MWMR multi-valued 1-atomic register from SWMR 1-safe bits, are complicated and are not practically useful for transforming algorithms that use strong type of registers into algorithms that use weak type of registers.

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Acknowledgments

We wish to thank the three anonymous referees and the associate editor Eric Ruppert for their constructive suggestions and corrections. Support is gratefully acknowledged from the National Science Foundation under grants CCF-1217921, CCF-1301926, and IIS-1447786, and the Department of Energy under Grant ER26116/DE-SC0008923.

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Authors and Affiliations

  1. MIT, Cambridge, MA, USA

    Nir Shavit

  2. Tel-Aviv University, Tel Aviv, Israel

    Nir Shavit

  3. The Interdisciplinary Center, P.O. Box 167, 46150, Herzliya, Israel

    Gadi Taubenfeld

Authors
  1. Nir Shavit
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  2. Gadi Taubenfeld
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Correspondence to Gadi Taubenfeld.

Additional information

A preliminary version of the results presented in this paper appeared in: (1) the Proceedings of the 22nd International Colloquium on Structural Information and Communication Complexity (SIROCCO 2015) [28], and (2) the Proceedings of the 14th International Conference on Distributed Computing and Networking (ICDCN 2013) [31].

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Shavit, N., Taubenfeld, G. The computability of relaxed data structures: queues and stacks as examples. Distrib. Comput. 29, 395–407 (2016). https://doi.org/10.1007/s00446-016-0272-0

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