An Optimal Self-stabilizing Firing Squad

  • Authors:

  • Danny Dolev;Ezra N. Hoch;Yoram Moses

  • Affiliations:

  • The Hebrew University of Jerusalem, Jerusalem, Israel;The Hebrew University of Jerusalem, Jerusalem, Israel;Technion--Israel Institute of Technology, Haifa, Israel

  • Venue:
  • SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
  • Year:
  • 2009

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Abstract

Consider a fully connected network where up to t processes may crash, and all processes start in an arbitrary memory state. The self-stabilizing firing squad problem consists of eventually guaranteeing simultaneous response to an external input. This is modeled by requiring that the non-crashed processes "fire" simultaneously if some correct process received an external "go " input, and that they only fire as a response to some process receiving such an input. This paper presents Fire-Squad , the first self-stabilizing firing squad algorithm. The Fire-Squad algorithm is optimal in two respects: (a) Once the algorithm is in a safe state, it fires in response to a go input as fast as any other algorithm does, and (b) Starting from an arbitrary state, it converges to a safe state as fast as any other algorithm does.