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DOI: 10.4230/LIPIcs.OPODIS.2015.18
Anonymous Obstruction-Free (n,k)-Set Agreement with n-k+1 Atomic Read/Write Registers

Authors: Zohir Bouzid, Michel Raynal, and Pierre Sutra

Published in: LIPIcs, Volume 46, 19th International Conference on Principles of Distributed Systems (OPODIS 2015)

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).
Cite as

Zohir Bouzid, Michel Raynal, and Pierre Sutra. Anonymous Obstruction-Free (n,k)-Set Agreement with n-k+1 Atomic Read/Write Registers. In 19th International Conference on Principles of Distributed Systems (OPODIS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 46, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{bouzid_et_al:LIPIcs.OPODIS.2015.18,
  author =	{Bouzid, Zohir and Raynal, Michel and Sutra, Pierre},
  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 =	{18:1--18:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-98-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{46},
  editor =	{Anceaume, Emmanuelle and Cachin, Christian and Potop-Butucaru, Maria},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2015.18},
  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}
}
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