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Poly-Logarithmic Adaptive Algorithms Require Unconditional Primitives

Authors Hagit Attiya, Arie Fouren

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Keywords
  • collect
  • atomic snapshot
  • renaming
  • fetch&inc
  • compare&swap

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Abstract

This paper studies the step complexity of adaptive algorithms using primitives stronger than reads and writes. We first consider unconditional primitives, like fetch&inc, which modify the value of the register to which they are applied, regardless of its current value. Unconditional primitives admit snapshot algorithms with O(log(k)) step complexity, where k is the total or the point contention. These algorithms combine a renaming algorithm with a mechanism for propagating values so they can be quickly collected.

When only conditional primitives, e.g., compare&swap or LL/SC, are used (in addition to reads and writes), we show that any collect algorithm must perform Omega(k) steps, in an execution with total contention k in O(log(log(n))). The lower bound applies for snapshot and renaming, both one-shot and long-lived. Note that there are snapshot algorithms whose step complexity is polylogarithmic in n using only reads and writes, but there are no adaptive algorithms whose step complexity is polylogarithmic in the contention, even when compare&swap and LL/SC are used.

Cite As Get BibTex

Hagit Attiya and Arie Fouren. Poly-Logarithmic Adaptive Algorithms Require Unconditional Primitives. In 19th International Conference on Principles of Distributed Systems (OPODIS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 46, pp. 36:1-36:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.OPODIS.2015.36

Author Details

Hagit Attiya
Arie Fouren

References

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