## Abstract

This paper presents two weak partially synchronous system models M ^{anti(n-k)} and M^{sink(n-k)} , which are just strong enough for solving k-set agreement: We introduce the generalized (n-k)-loneliness failure detector L}(k), which we first prove to be sufficient for solving k-set agreement, and show that L(k) but not L(k-1) can be implemented in both models. M^{anti(n-k)} and M^{sink(n-k)} are hence the first message passing models that lie between models where Ω (and therefore consensus) can be implemented and the purely asynchronous model. We also address k-set agreement in anonymous systems, that is, in systems where (unique) process identifiers are not available. Since our novel k -set agreement algorithm using L(k) also works in anonymous systems, it turns out that the loneliness failure detector L=L(n-1) introduced by Delporte et al. is also the weakest failure detector for set agreement in anonymous systems. Finally, we analyze the relationship between L(k) and other failure detectors suitable for solving k-set agreement.

Original language | English (US) |
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Article number | 6482555 |

Pages (from-to) | 1078-1088 |

Number of pages | 11 |

Journal | IEEE Transactions on Parallel and Distributed Systems |

Volume | 25 |

Issue number | 4 |

DOIs | |

State | Published - Apr 2014 |

Externally published | Yes |

## Keywords

- Distributed systems
- models of computation

## ASJC Scopus subject areas

- Signal Processing
- Hardware and Architecture
- Computational Theory and Mathematics