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

Authors Zohir Bouzid, Michel Raynal, Pierre Sutra



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LIPIcs.OPODIS.2015.18.pdf
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Zohir Bouzid
Michel Raynal
Pierre Sutra

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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)
https://doi.org/10.4230/LIPIcs.OPODIS.2015.18

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).
Keywords
  • Anonymous processes
  • Asynchronous system
  • Atomic read/write register
  • Consensus
  • Fault-tolerance
  • $k$-Set agreement
  • Obstruction-freedom
  • Upper bound

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