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Long-Lived Counters with Polylogarithmic Amortized Step Complexity

Authors Mirza Ahad Baig, Danny Hendler, Alessia Milani, Corentin Travers

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Subject Classification

ACM Subject Classification
  • Theory of computation → Shared memory algorithms
  • Theory of computation → Concurrent algorithms
Keywords
  • Shared Memory
  • Wait-freedom
  • Counter
  • Amortized Complexity
  • Concurrent Objects

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Abstract

A shared-memory counter is a well-studied and widely-used concurrent object. It supports two operations: An Inc operation that increases its value by 1 and a Read operation that returns its current value. Jayanti, Tan and Toueg [Jayanti et al., 2000] proved a linear lower bound on the worst-case step complexity of obstruction-free implementations, from read and write operations, of a large class of shared objects that includes counters. The lower bound leaves open the question of finding counter implementations with sub-linear amortized step complexity.
In this paper, we address this gap. We present the first wait-free n-process counter, implemented using only read and write operations, whose amortized operation step complexity is O(log^2 n) in all executions. This is the first non-blocking read/write counter algorithm that provides sub-linear amortized step complexity in executions of arbitrary length. Since a logarithmic lower bound on the amortized step complexity of obstruction-free counter implementations exists, our upper bound is optimal up to a logarithmic factor.

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Mirza Ahad Baig, Danny Hendler, Alessia Milani, and Corentin Travers. Long-Lived Counters with Polylogarithmic Amortized Step Complexity. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.DISC.2019.3

Author Details

Mirza Ahad Baig
  • LaBRI, Bordeaux INP, France
  • CNRS, ReLaX, UMI2000, Siruseri, India
  • Chennai Mathematical Institute, Siruseri, India
Danny Hendler
  • Ben-Gurion University of the Negev, Beer-Sheva, Israel
Alessia Milani
  • LaBRI, Bordeaux INP, France
Corentin Travers
  • LaBRI, Bordeaux INP, France

Funding

Mirza Ahad Baig, Alessia Milani and Corentin Travers are supported by ANR projects Descartes and FREDDA. Mirza Ahad Baig is additionally supported by UMI Relax. Danny Hendler is supported by the Israel Science Foundation (grant 380/18).

Acknowledgements

We thank the anonymous reviewers for their many helpful comments.

References

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