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## A Topological Treatment of Early-Deciding Set-Agreement (2008)

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1946 | Distributed Algorithms - Lynch - 1996 |

1707 | Impossibility of distributed consensus with one faulty process
- Fischer, Lynch, et al.
- 1985
(Show Context)
Citation Context ...own value, possibly different from all other values, to agree on less than k among all initial values, despite the crash of some of the processes. The problem is a natural generalization of consensus =-=[9]-=-, which correspond to the case where k = 1. Most studies of the time complexity of k-set-agreement focused on worst-case global decision bounds. Chaudhuri et al. in [4], Herlihy et al. in [14], and Ga... |

510 | Consensus in the presence of partial synchrony
- Dwork, Lynch, et al.
- 1988
(Show Context)
Citation Context ...wer bound on the time complexity of early-deciding set-agreement in a synchronous model of distributed computation. This lower bound also holds for synchronous runs of an eventually synchronous model =-=[8]-=- but we conjecture a larger lower bound for such runs. Determining such a bound, which would generalize the result of [6], is an intriguing open problem. As we discussed in the related work section, a... |

203 |
Munkres. Elements of Algebraic Topology
- R
(Show Context)
Citation Context ...cally, the protocol complexes of which we compute the connectivity can be viewed as a union of n-dimensional pseudospheres which makes it possible to apply (a corollary of) the Mayer-Vietoris theorem =-=[17]-=-. We also use here a theorem from [12], which itself generalizes Theorem 9 and Theorem 11 of [14]. The main originality in our work is the introduction of our early-deciding operator, which is key to ... |

163 |
Generalized FLP impossibility result for tresilient asynchronous computations
- Borowsky, Gafni
- 1993
(Show Context)
Citation Context ...s might crash, assuming a restricted class of distributed protocols called stable vector protocols. In 1993, three independent teams of researchers, namely Herlihy and Shavit [15], Borowsky and Gafni =-=[1]-=-, and Saks and Zaharoglou [18], proved, concurrently, that k-set-agreement is impossible in an asynchronous system when k processes may crash. All used topological arguments for showing the results. (... |

151 | The topological structure of asynchronous computability
- Herlihy, Shavit
- 1999
(Show Context)
Citation Context ...mplexes and complexes It is convenient to model a global state of a system of n + 1 processes as an n-dimensional simplex S n = (s0, ..., sn), where si = 〈pi, vi〉 defines local state vi of process pi =-=[15]-=-. We say that the vertexes s0, ..., sn span the simplex S n . We say that a simplex T is a face of a simplex S if all vertexes of T are vertexes of S. A set of global states is modeled as a set of sim... |

110 | More choices allow more faults: Set consensus problems in totally asynchronous systems
- Chaudhuri
- 1993
(Show Context)
Citation Context ...needed to reach this degree of coordination in a given run of the system, and the actual number of processes that crash in that run. We do so by considering the time complexity of the k-set-agreement =-=[3]-=- (or simply setagreement) problem. The problem consists for the processes of the system, each starting with its own value, possibly different from all other values, to agree on less than k among all i... |

104 |
Wait-free k-set agreement is impossible: The topology of public knowledge
- Saks, Zaharoglou
(Show Context)
Citation Context ...tricted class of distributed protocols called stable vector protocols. In 1993, three independent teams of researchers, namely Herlihy and Shavit [15], Borowsky and Gafni [1], and Saks and Zaharoglou =-=[18]-=-, proved, concurrently, that k-set-agreement is impossible in an asynchronous system when k processes may crash. All used topological arguments for showing the results. (Herlihy and Shavit later intro... |

92 | Early stopping in Byzantine agreement
- Dolev, Reischuk, et al.
- 1990
(Show Context)
Citation Context ...non-crashed) processes to decide. This (worst-case global decision) bound is tight and there are indeed protocols that match it, e.g., [4]. This paper studies the complexity of early global decisions =-=[5]-=-. Assuming a known maximum number of t processes that may crash, early-deciding protocols are those that takes advantage of the effective number f ≤ t of failures in any run. In particular, for runs w... |

68 | On the Cost of Fault-Tolerant Consensus When There Are No Faults -- A Tutorial. MIT
- Keidar, Rajsbaum
(Show Context)
Citation Context ... bound is thus tight. Our result generalizes, on the one hand, results on worst-case global decisions for set agreement [4, 14], and on the other hand, results on early global decisions for consensus =-=[16, 2]-=-. As we discuss in the related work section, our bound is also complementary to a recent result on early local decisions for set-agreement [11] with an unbounded number of processes. To prove our lowe... |

54 | Rounds-by-rounds fault detectors: unifying synchrony and asynchrony
- Gafni
- 1998
(Show Context)
Citation Context ... correspond to the case where k = 1. Most studies of the time complexity of k-set-agreement focused on worst-case global decision bounds. Chaudhuri et al. in [4], Herlihy et al. in [14], and Gafni in =-=[10]-=-, have shown that, for any k-set agreement protocol tolerating at most t process crashes, there exists a run in which ⌊t/k⌋ + 1 communication rounds are needed for all correct (non-crashed) processes ... |

44 | Uniform consensus is harder than consensus (extended abstract
- Charron-Bost, Schiper
- 2000
(Show Context)
Citation Context ... bound is thus tight. Our result generalizes, on the one hand, results on worst-case global decisions for set agreement [4, 14], and on the other hand, results on early global decisions for consensus =-=[16, 2]-=-. As we discuss in the related work section, our bound is also complementary to a recent result on early local decisions for set-agreement [11] with an unbounded number of processes. To prove our lowe... |

31 | Algebraic spans
- Herlihy, Rajsbaum
- 1995
(Show Context)
Citation Context ...ogical arguments for showing the results. (Herlihy and Shavit later introduced in [15] a complete topological characterization of asynchronous shared-memory runs, using the concept of algebraic spans =-=[13]-=- for showing the sufficiency of the characterization.) Chaudhuri et al. in [4], and Herlihy et al. in [14], then investigated the k-set-agreement problem in the synchronous message-passing system, and... |

27 | Unifying synchronous and asynchronous message-passing models
- HERLIHY, RAJSBAUM, et al.
- 1998
(Show Context)
Citation Context ...onsensus [9], which correspond to the case where k = 1. Most studies of the time complexity of k-set-agreement focused on worst-case global decision bounds. Chaudhuri et al. in [4], Herlihy et al. in =-=[14]-=-, and Gafni in [10], have shown that, for any k-set agreement protocol tolerating at most t process crashes, there exists a run in which ⌊t/k⌋ + 1 communication rounds are needed for all correct (non-... |

22 | Tight Bounds for k-Set Agreement
- Chaudhuri, Herlihy, et al.
- 1993
(Show Context)
Citation Context ...ral generalization of consensus [9], which correspond to the case where k = 1. Most studies of the time complexity of k-set-agreement focused on worst-case global decision bounds. Chaudhuri et al. in =-=[4]-=-, Herlihy et al. in [14], and Gafni in [10], have shown that, for any k-set agreement protocol tolerating at most t process crashes, there exists a run in which ⌊t/k⌋ + 1 communication rounds are need... |

17 | The inherent price of indulgence
- Dutta, Guerraoui
- 2002
(Show Context)
Citation Context ...lower bound also holds for synchronous runs of an eventually synchronous model [8] but we conjecture a larger lower bound for such runs. Determining such a bound, which would generalize the result of =-=[6]-=-, is an intriguing open problem. As we discussed in the related work section, although, at first glance, the local decision lower bound presented in [11] seems to imply a global decision on k-set-agre... |

7 | From a static impossibility to an adaptive lower bound: the complexity of early deciding set agreement
- Gafni, Guerraoui, et al.
- 2005
(Show Context)
Citation Context ...he system where f processes fail. Interestingly, there is a protocol through which all correct processes decide within min(⌊f/k⌋ + 2, ⌊t/k⌋ + 1) rounds in every run in which at most f processes crash =-=[11]-=-.sWe prove in this paper a lower bound of min(⌊f/k⌋ + 2, ⌊t/k⌋ + 1) on the round complexity needed to reach a global decision in any run in which at most f processes crash. The bound is thus tight. Ou... |

4 | A note on Set Agreement with Omission Failures
- Guerraoui, Kouznetsov, et al.
(Show Context)
Citation Context ... we compute the connectivity can be viewed as a union of n-dimensional pseudospheres which makes it possible to apply (a corollary of) the Mayer-Vietoris theorem [17]. We also use here a theorem from =-=[12]-=-, which itself generalizes Theorem 9 and Theorem 11 of [14]. The main originality in our work is the introduction of our early-deciding operator, which is key to showing that the connectivity is prese... |

3 |
Tight lower bounds on early local decisions in uniform consensus
- Dutta, Guerraoui, et al.
- 2003
(Show Context)
Citation Context ...th a fixed number of processes. On the other hand, the bound of [11] states that no single process may decide within ⌊f/k⌋ + 1 rounds. In this sense, the result of [11] characterizes a local decision =-=[7]-=- bound and is in this sense stronger than the bound of this paper. Coming up with a bound on local decisions and a bounded number of processes is an open question that is out of the scope of this pape... |