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DOI: 10.4230/LIPIcs.OPODIS.2016.32

Step Optimal Implementations of Large Single-Writer Registers

Authors: Tian Ze Chen and Yuanhao Wei

Published in: LIPIcs, Volume 70, 20th International Conference on Principles of Distributed Systems (OPODIS 2016)

Abstract

We present two wait-free algorithms for simulating an l-bit single-writer register from k-bit single-writer registers, for any k >= 1. Our first algorithm has big-theta(l/k) step complexity for both Read and Write and uses big-theta (4^(l-k)) registers. An interesting feature of the algorithm is that Read operations do not write to shared variables. Our second algorithm has big-theta (l/k + (log n)/k) step complexity for both Read and Write, where n is the number of readers, but uses only big-theta (nl/k + n(log n)/k) registers. Combining both algorithms gives an implementation with big-theta (l/k) step complexity using big-theta (nl/k) space for any 1 <= k < l. We also prove that any implementation with big-O (l/k) step complexity for Read requires big-omega (l/k) step complexity for Write. Since reading l-bits requires at least ceiling(l/k) reads of k-bit registers, our lower bound shows that our implementation is step optimal.

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Tian Ze Chen and Yuanhao Wei. Step Optimal Implementations of Large Single-Writer Registers. In 20th International Conference on Principles of Distributed Systems (OPODIS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 70, pp. 32:1-32:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{chen_et_al:LIPIcs.OPODIS.2016.32,
  author =	{Chen, Tian Ze and Wei, Yuanhao},
  title =	{{Step Optimal Implementations of Large Single-Writer Registers}},
  booktitle =	{20th International Conference on Principles of Distributed Systems (OPODIS 2016)},
  pages =	{32:1--32:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-031-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{70},
  editor =	{Fatourou, Panagiota and Jim\'{e}nez, Ernesto and Pedone, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2016.32},
  URN =		{urn:nbn:de:0030-drops-71010},
  doi =		{10.4230/LIPIcs.OPODIS.2016.32},
  annote =	{Keywords: atomic register, regular register, wait-free implementation, single writer, optimal}
}

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Step Optimal Implementations of Large Single-Writer Registers

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