51/2009 : Weak Synchrony Models and Failure Detectors for Message Passing k-Set Agreement

RR Number

51/2009

Conference

To appear in: Proceedings of the International Conference on Principles of Distributed Systems (OPODIS'09), Nimes, France, 2009.

Author(s)

Martin Biely, Peter Robinson, Ulrich Schmid

Abstract

The recent discovery of the weakest failure detector L for message passing set agreement has renewed the interest in exploring the border between solvable and unsolvable problems in message passing systems. This paper contributes to this research by introducing two novel system models MAnti and MSink with very weak synchrony requirements, where L can be implemented. To the best of our knowledge, they are the first message passing models where set agreement is solvable but consensus is not. We also generalize L by a novel ``(n-k)-loneliness'' failure detector L(k), which allows to solve k-set agreement but not (k-1)-set agreement. We also present an algorithm that solves k-set agreement with L(k), which is anonymous in that it does not require unique process identifiers. This reveals that L is also the weakest failure detector for anonymous set agreement. Finally, we analyze the relationship between L(k) and and other failure detectors, namely the limited scope failure detector S_{n-k+1} and the quorum failure detector Sigma.

Bibtex

@inProceedings{BRS09:opodis,
  title={Weak Synchrony Models and Failure Detectors for Message Passing $k$-Set Agreement},
  author={Martin Biely and Peter Robinson and Ulrich Schmid},
  booktitle =    {Proceedings of the International Conference on
                  Principles of Distributed Systems (OPODIS'09)},
  year =         2009,
  address =      {Nimes, France},
  month =        {Dec},
  series =       {LNCS},
  publisher =    {Springer Verlag},
  note = "(to appear)",
}

Download

Get paper.pdf - Adobe PDF-format, (242.26 KB; posted at September 18 2009; )

Get paper.pdf - Adobe PDF-format, (242.26 KB; posted at September 18 2009; )