(anti−Ω × Σz)-based k-set Agreement Algorithms
نویسندگان
چکیده
This paper considers the k-set agreement problem in a crash-prone asynchronous message passing system enriched with failure detectors. Two classes of failure detectors have been previously identified as necessary to solve asynchronous k-set agreement: the class anti-leader anti−Ω and the weak-quorum class Σk. The paper investigates the families of failure detector (anti−Ωx)1≤x≤n and (Σz)1≤z≤n. It characterizes in an n processes system equipped with failure detectors anti−Ω and Σz for which values of k, x and z k-set-agreement can be solved. While doing so, the paper (1) disproves previous conjunctures about the weakest failure detector to solve k-set-agreement in the asynchronous message passing model and, (2) introduces the first indulgent algorithm that tolerates a majority of processes failures.
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In the k-set agreement task, n processes propose values, and have to decide on at most k of these values. In particular, consensus is 1-set agreement. In PODC 2008 Zieliński showed that the anti−Ω failure detector is necessary and sufficient to solve (n − 1)-set agreement in an asynchronous read/write shared memory system where at most t processes can fail by crashing, t = n− 1. In this paper i...
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