Abstract
This paper considers the k-set-agreement problem in a synchronous message passing distributed system where up to t processes can fail by crashing. We determine the number of communication rounds needed for all correct processes to reach a decision in a given run, as a function of k, the degree of coordination, and f ≤t the number of processes that actually fail in the run. We prove a lower bound of \(\textit{min}(\lfloor{f/k}\rfloor+2,\lfloor{t/k}\rfloor+1)\) rounds. Our proof uses simple topological tools to reason about runs of a full information set-agreement protocol. In particular, we introduce a topological operator, which we call the early deciding operator, to capture rounds where k processes fail but correct processes see only k–1 failures.
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Guerraoui, R., Herlihy, M., Pochon, B. (2006). A Topological Treatment of Early-Deciding Set-Agreement. In: Shvartsman, M.M.A.A. (eds) Principles of Distributed Systems. OPODIS 2006. Lecture Notes in Computer Science, vol 4305. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11945529_3
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DOI: https://doi.org/10.1007/11945529_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-49990-9
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