Leader Election is an important primitive in fault-tolerant distributed computing. In this paper, we propose a new, weaker specification of the Leader Election problem motivated by the design of Primary-Backup protocols for receive-omission failures. The lower bound for this problem assuming a threshold on the number of failures has been known for many years, but this bound was not known to be tight. We repeat this result and generalize the bound to our model of dependent failures. We then propose and show the correctness of an algorithm that solves Weak Leader Election. There are three main contributions in the derivation of this algorithm. First, we show that a known lower bound is actually tight. Second, we design it using our model of dependent failures based on cores and survivor sets, thus enabling the use of such an algorithm in heterogeneous settings and illustrating the process of designing algorithms in this model. Finally, due to weaker requirements, this algorithm uses less replication than previous algorithms.
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