Failure detector class Ω k has been defined in [17] as an extension to failure detector \u00adΩ, and an algorithm has been given in [15] to solve k-set agreement using Ω \u00adk in asynchronous message-passing systems. In this paper, we extend these previous works in two directions. First, we define two new classes of failure detectors Ω’ \u00adk and Ω” \u00adk , which are new ways of extending Ω\u00ad, and show that they are equivalent to Ω \u00adk . Class Ω’ \u00adk is more flexible than Ω \u00adk in that it does not require the outputs to stabilize eventually, while class Ω” \u00adk does not refer to other processes in its outputs and thus serves as a good basis for the partitioned failure detectors we introduce in [6]. Second, we present a new algorithm that solves k-set agreement using Ω” \u00adk when a majority of processes do not crash. The algorithm is a faithful extension of the Paxos algorithm [11], and thus it inherits the efficiency, flexibility, and robustness of the Paxos algorithm. In particular, it has better message complexity than the algorithm in [15]. Both the new failure detectors and the new algorithm enrich our understanding of the k-set agreement problem. In particular, they serve as the basis of our study on partitioned failure detectors for k-set agreement [6].<\/p>\n","protected":false},"excerpt":{"rendered":"
Failure detector class Ω k has been defined in [17] as an extension to failure detector \u00adΩ, and an algorithm has been given in [15] to solve k-set agreement using Ω \u00adk in asynchronous message-passing systems. In this paper, we extend these previous works in two directions. 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