Abstract
We study the message complexity of the problem of distributively electing a leader in chordal rings. Such networks consist of a basic ring with additional links, the extreme cases being the oriented ring and the complete graph with a full sense of direction. We present a general election algorithm for these networks, and prove its optimality. As a corollary, we show thatO(logn) chords at each processor suffice to obtain an algorithm that uses at mostO(n) messages; this improves and extends a previous work, where an algorithm, also usingO(n) messages, was suggested for the case where alln-1 chords exist (the oriented complete network).
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Communicated by Israel Cidon and Inder S. Gopal.
The work of this author was supported in part by the Natural Sciences and Engineering Research Council of Canada under Grant No. A2415.
The work of this author was supported in part by Technion Research Grant No. 120-0641.
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Attiya, H., van Leeuwen, J., Santoro, N. et al. Efficient elections in chordal ring networks. Algorithmica 4, 437–446 (1989). https://doi.org/10.1007/BF01553900
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DOI: https://doi.org/10.1007/BF01553900