Early-Stopping k-Set Agreement in Synchronous Systems Prone to Any Number of Process Crashes

The k set agreement problem is a generalization of the consensus problem each process proposes a value and each non faulty process has to decide a value such that a decided value is a proposed value and no more than k di erent values are decided This paper presents a surprisingly simple k set agreement protocol for synchronous systems where up to t n processes can crash where n is the total number of processes The proposed protocol is the rst early stopping k set agreement protocol that does not impose a constraint on t It allows the processes to decide and stop by min bf kc bt kc rounds where f is the number of actual crashes f t In addition to its conceptual simplicity the protocol has an additional noteworthy feature namely it is particularly e cient in common case scenarios This comes from the fact that it is based on a mechanism that allows the processes to take into account the actual pattern of failures and not only their number thereby allowing the processes to decide in much less than bf kc rounds in a lot of cases