A topological treatment of early-deciding set-agreement

Authors:
Rachid Guerraoui;Maurice Herlihy;Bastian Pochon
Affiliations:
School of Computer and Communication Sciences, EPFL;Computer Science Department, Brown University;School of Computer and Communication Sciences, EPFL
Venue:
OPODIS'06 Proceedings of the 10th international conference on Principles of Distributed Systems
Year:
2006

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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 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.