Communication-efficient and crash-quiescent Omega with unknown membership

The failure detector class Omega (@W) provides an eventual leader election functionality, i.e., eventually all correct processes permanently trust the same correct process. An algorithm is communication-efficient if the number of links that carry messages forever is bounded by n, being n the number of processes in the system. It has been defined that an algorithm is crash-quiescent if it eventually stops sending messages to crashed processes. In this regard, it has been recently shown the impossibility of implementing @W crash quiescently without a majority of correct processes. We say that the membership is unknown if each process p"i only knows its own identity and the number of processes in the system (that is, i and n), but p"i does not know the identity of the rest of processes of the system. There is a type of link (denoted by ADD link) in which a bounded (but unknown) number of consecutive messages can be delayed or lost. In this work we present the first implementation (to our knowledge) of @W in partially synchronous systems with ADD links and with unknown membership. Furthermore, it is the first implementation of @W that combines two very interesting properties: communication-efficiency and crash-quiescence when the majority of processes are correct. Finally, we also obtain with the same algorithm a failure detector (@?P@?) such that every correct process eventually and permanently outputs the set of all correct processes.