Narrowing power vs efficiency in synchronous set agreement: Relationship, algorithms and lower bound

  • Authors:

  • Achour Mostéfaoui;Michel Raynal;Corentin Travers

  • Affiliations:

  • IRISA, Campus de Beaulieu, 35042 Rennes Cedex, France;IRISA, Campus de Beaulieu, 35042 Rennes Cedex, France;IRISA, Campus de Beaulieu, 35042 Rennes Cedex, France

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2010

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Abstract

The k-set agreement problem is a generalization of the uniform consensus problem: each process proposes a value, and each non-faulty process has to decide a value such that a decided value is a proposed value, and at most k different values are decided. It has been shown that any algorithm that solves the k-set agreement problem in synchronous systems that can suffer up to t crash failures requires @?tk@?+1 rounds in the worst case. It has also been shown that it is possible to design early deciding algorithms where no process decides and halts after min(@?fk@?+2,@?tk@?+1) rounds, where f is the number of actual crashes in a run (0@?f@?t). This paper explores a new direction to solve the k-set agreement problem in a synchronous system. It considers that the system is enriched with base objects (denoted has [m,@?]_SA objects) that allow solving the @?-set agreement problem in a set of m processes (m