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An Almost Tight RMR Lower Bound for Abortable Test-And-Set

Authors Aryaz Eghbali, Philipp Woelfel

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ACM Subject Classification
  • Theory of computation → Shared memory algorithms
Keywords
  • Abortability
  • Test-And-Set
  • Leader Election
  • Compare-and-Swap
  • RMR Complexity
  • Lower Bound

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Abstract

We prove a lower bound of Omega(log n/log log n) for the remote memory reference (RMR) complexity of abortable test-and-set (leader election) in the cache-coherent (CC) and the distributed shared memory (DSM) model. This separates the complexities of abortable and non-abortable test-and-set, as the latter has constant RMR complexity [Wojciech Golab et al., 2010].
Golab, Hendler, Hadzilacos and Woelfel [Wojciech M. Golab et al., 2012] showed that compare-and-swap can be implemented from registers and test-and-set objects with constant RMR complexity. We observe that a small modification to that implementation is abortable, provided that the used test-and-set objects are atomic (or abortable). As a consequence, using existing efficient randomized wait-free implementations of test-and-set [George Giakkoupis and Philipp Woelfel, 2012], we obtain randomized abortable compare-and-swap objects with almost constant (O(log^* n)) RMR complexity.

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Aryaz Eghbali and Philipp Woelfel. An Almost Tight RMR Lower Bound for Abortable Test-And-Set. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 21:1-21:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.DISC.2018.21

Author Details

Aryaz Eghbali
  • Department of Computer Science, University of Calgary, Canada
Philipp Woelfel
  • Department of Computer Science, University of Calgary, Canada

Funding

This research was undertaken, in part, thanks to funding from the Canada Research Chairs program and from the Discovery Grants program of the Natural Sciences and Engineering Research Council of Canada (NSERC).

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