License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.OPODIS.2015.36
URN: urn:nbn:de:0030-drops-66793
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6679/
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Attiya, Hagit ; Fouren, Arie

Poly-Logarithmic Adaptive Algorithms Require Unconditional Primitives

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LIPIcs-OPODIS-2015-36.pdf (0.5 MB)

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.

BibTeX - Entry

@InProceedings{attiya_et_al:LIPIcs:2016:6679,
  author =	{Hagit Attiya and Arie Fouren},
  title =	{{Poly-Logarithmic Adaptive Algorithms Require Unconditional Primitives}},
  booktitle =	{19th International Conference on Principles of Distributed Systems (OPODIS 2015)},
  pages =	{1--16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-98-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{46},
  editor =	{Emmanuelle Anceaume and Christian Cachin and Maria Potop-Butucaru},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6679},
  URN =		{urn:nbn:de:0030-drops-66793},
  doi =		{10.4230/LIPIcs.OPODIS.2015.36},
  annote =	{Keywords: collect, atomic snapshot, renaming, fetch&inc, compare&swap}
}

Keywords: collect, atomic snapshot, renaming, fetch&inc, compare&swap
Collection: 19th International Conference on Principles of Distributed Systems (OPODIS 2015)
Issue Date: 2016
Date of publication: 13.10.2016

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