Abstract
This paper considers the leader election problem (LEP) in asynchronous complete networks with undetectable fail-stop failures. Especially, it is discussed whether presence of a global sense of direction affects the message complexity of LEP in faulty networks. For a complete network of n processors where k processors start the algorithm spontaneously and at most f p (<n/2) processors are faulty, this paper shows
(1) the message complexity of LEP is Θ(n+k f p ), if the complete network has a global sense of direction.
It is already known that LEP requires Ω(n log k+k f p ) message exchanges, if the complete network has no global sense of direction. Therefore, our result implies that the message complexity of LEP can be greatly reduced by using a global sense of direction in faulty networks as well as in reliable networks. For a complete network with at most f l (<n−1) faulty links (and no faulty processor), this paper also shows the similar result:
(2) the message complexity of LEP is Θ(n+k f l +f l log f l ), if the complete network has a global sense of direction.
This work was supported in part by The Mazda Foundation's Research Grant and The Inamori Foundation's Research Grant.
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© 1989 Springer-Verlag Berlin Heidelberg
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Masuzawa, T., Nishikawa, N., Hagihara, K., Tokura, N. (1989). Optimal fault-tolerant distributed algorithms for election in complete networks with a global sense of direction. In: Bermond, JC., Raynal, M. (eds) Distributed Algorithms. WDAG 1989. Lecture Notes in Computer Science, vol 392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51687-5_41
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DOI: https://doi.org/10.1007/3-540-51687-5_41
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