A channel from a process p to a process q satisfies the ADD property if there are constants K and D, unknown to the processes, such that in any sequence of K consecutive messages sent by p to q, at least one of them is delivered to q at most D time units after it has been sent. This paper studies implementations of an eventual leader, namely, an {Omega} failure detector, in an arbitrarily connected network of eventual ADD channels, where processes may fail by crashing. It first presents an algorithm that assumes that processes initially know n, the total number of processes, sending messages of size O( log n). Then, it presents a second algorithm that does not assume the processes know n. Eventually the size of the messages sent by this algorithm is also O( log n). These are the first implementations of leader election in the ADD model. In this model, only eventually perfect failure detectors were considered, sending messages of size O(n log n).
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