Adaptive timeliness of consensus in presence of crash and timing faults

  • Authors:

  • Taisuke Izumi;Akinori Saitoh;Toshimitsu Masuzawa

  • Affiliations:

  • Graduate School of Engineering, Nagoya Institute of Technology, Gokiso, Showa, Nagoya, Aichi 466-8555, Japan;Faculty of Environmental and Information Studies, Tottori University of Environmental Studies, 1-1-1, Wakabadai-Kita, Tottori 689-1111, Japan;Graduate School of Engineering, Nagoya Institute of Technology, Gokiso, Showa, Nagoya, Aichi 466-8555, Japan

  • Venue:
  • Journal of Parallel and Distributed Computing
  • Year:
  • 2007

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Abstract

The @D-timed uniform consensus is a stronger variant of the traditional consensus and it satisfies the following additional property: every correct process terminates its execution within a constant time @D (@D-timeliness), and no two processes decide differently (uniformity). In this paper, we consider the @D-timed uniform consensus problem in presence of f"c crash processes and f"t timing-faulty processes, and propose a @D-timed uniform consensus algorithm. The proposed algorithm is adaptive in the following sense: it solves the @D-timed uniform consensus when at least f"t+1 correct processes exist in the system. If the system has less than f"t+1 correct processes, the algorithm cannot solve the @D-timed uniform consensus. However, as long as f"t+1 processes are non-crashed, the algorithm solves (non-timed) uniform consensus. We also investigate the maximum number of faulty processes that can be tolerated. We show that any @D-timed uniform consensus algorithm tolerating up to f"t timing-faulty processes requires that the system has at least f"t+1 correct processes. This impossibility result implies that the proposed algorithm attains the maximum resilience about the number of faulty processes. We also show that any @D-timed uniform consensus algorithm tolerating up to f"t timing-faulty processes cannot solve the (non-timed) uniform consensus when the system has less than f"t+1 non-crashed processes. This impossibility result implies that our algorithm attains the maximum adaptiveness.