Weak Synchrony Models and Failure Detectors for Message Passing (k-)Set Agreement

  • Authors:

  • Martin Biely;Peter Robinson;Ulrich Schmid

  • Affiliations:

  • Embedded Computing Systems Group, Technische Universität Wien, Austria and LIX, Ecole polytechnique, France;Embedded Computing Systems Group, Technische Universität Wien, Austria;Embedded Computing Systems Group, Technische Universität Wien, Austria

  • Venue:
  • OPODIS '09 Proceedings of the 13th International Conference on Principles of Distributed Systems
  • Year:
  • 2009

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Abstract

The recent discovery of the weakest failure detector ${\mathcal{L}}$ 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 ${\mathcal{M}^\text{anti}}$ and ${\mathcal{M}^\text{sink}}$ with very weak synchrony requirements, where ${\mathcal{L}}$ 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 ${\mathcal{L}}$ by a novel "(n ***k )-loneliness" failure detector ${\mathcal{L}}(k)$, which allows to solve k -set agreement but not (k ***1)-set agreement. We also present an algorithm that solves k -set agreement with ${\mathcal{L}}(k)$, which is anonymous in that it does not require unique process identifiers. This reveals that ${\mathcal{L}}$ is also the weakest failure detector for anonymous set agreement. Finally, we analyze the relationship between ${\mathcal{L}}(k)$ and other failure detectors, namely the limited scope failure detector ${\mathcal{S}}_{n-k+1}$ and the quorum failure detector Σ.