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.2015.18
URN: urn:nbn:de:0030-drops-66092
URL: https://drops.dagstuhl.de/opus/volltexte/2016/6609/
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Bouzid, Zohir ; Raynal, Michel ; Sutra, Pierre

Anonymous Obstruction-Free (n,k)-Set Agreement with n-k+1 Atomic Read/Write Registers

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LIPIcs-OPODIS-2015-18.pdf (0.6 MB)


Abstract

The k-set agreement problem is a generalization of the consensus problem. Namely, assuming that each process proposes a value, every non-faulty process should decide one of the proposed values, and no more than k different values should be decided. This is a hard problem in the sense that we cannot solve it in an asynchronous system, as soon as k or more processes may crash. One way to sidestep this impossibility result consists in weakening the termination property, requiring that a process must decide a value only if it executes alone during a long enough period of time. This is the well-known obstruction-freedom progress condition.

Consider a system of n anonymous asynchronous processes that communicate through atomic read/write registers, and such that any number of them may crash. In this paper, we address and solve the challenging open problem of designing an obstruction-free k-set agreement algorithm using only (n-k+1) atomic registers. From a shared memory cost point of view, our algorithm is the best algorithm known so far, thereby establishing a new upper bound on the number of registers needed to solve the problem, and in comparison to the previous upper bound, its gain is (n-k) registers. We then extend this algorithm into a space-optimal solution for the repeated version of k-set agreement, and an x-obstruction-free solution that employs 0(n-k+x) atomic registers (with 1 <= x <= k < n).

BibTeX - Entry

@InProceedings{bouzid_et_al:LIPIcs:2016:6609,
  author =	{Zohir Bouzid and Michel Raynal and Pierre Sutra},
  title =	{{Anonymous Obstruction-Free (n,k)-Set Agreement with n-k+1 Atomic Read/Write Registers}},
  booktitle =	{19th International Conference on Principles of Distributed Systems (OPODIS 2015)},
  pages =	{1--17},
  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/2016/6609},
  URN =		{urn:nbn:de:0030-drops-66092},
  doi =		{10.4230/LIPIcs.OPODIS.2015.18},
  annote =	{Keywords: Anonymous processes, Asynchronous system, Atomic read/write register, Consensus, Fault-tolerance, $k$-Set agreement, Obstruction-freedom, Upper bound}
}

Keywords: Anonymous processes, Asynchronous system, Atomic read/write register, Consensus, Fault-tolerance, $k$-Set agreement, Obstruction-freedom, Upper bound
Collection: 19th International Conference on Principles of Distributed Systems (OPODIS 2015)
Issue Date: 2016
Date of publication: 13.10.2016


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