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

Authors Aryaz Eghbali, Philipp Woelfel



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

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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

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.

Subject Classification

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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