Set agreement and the loneliness failure detector in crash-recovery systems

The set agreement problem states that from n proposed values at most n-1 can be decided. Traditionally, this problem is solved using a failure detector in asynchronous systems where processes may crash but not recover, where processes have different identities, and where all processes initially know the membership. In this paper we study the set agreement problem and the weakest failure detector L used to solve it in asynchronous message passing systems where processes may crash and recover, with homonyms (i.e., processes may have equal identities) and without a complete initial knowledge of the membership.

Communication-efficient and crash-quiescent Omega with unknown membership

The failure detector class Omega (Ω) 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 Ω crash quiescently without a majority of correct processes. We say that the membership is unknown if each process pi only knows its own identity and the number of processes in the system (that is, i and n), but pi 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 Ω in partially synchronous systems with ADD links and with unknown membership. Furthermore, it is the first implementation of Ω 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 () such that every correct process eventually and permanently outputs the set of all correct processes.

Failure Detectors in Homonymous Distributed Systems (with an Application to Consensus).

This paper is on homonymous distributed systems where processes are prone to crash failures and have no initial knowledge of the system membership (?homonymous? means that several processes may have the same identi?er). New classes of failure detectors suited to these systems are ?rst de?ned. Among them, the classes H? and H? are introduced that are the homonymous counterparts of the classes ? and ?, respectively. (Recall that the pair h?,?i de?nes the weakest failure detector to solve consensus.) Then, the paper shows how H? and H? can be implemented in homonymous systems without membership knowledge (under different synchrony requirements). Finally, two algorithms are presented that use these failure detectors to solve consensus in homonymous asynchronous systems where there is no initial knowledge ofthe membership. One algorithm solves consensus with hH?, H?i, while the other uses only H?, but needs a majority of correct processes. Observe that the systems with unique identi?ers and anonymous systems are extreme cases of homonymous systems from which follows that all these results also apply to these systems. Interestingly, the new failure detector class H? can be implemented with partial synchrony, while the analogous class A? de?ned for anonymous systems can not be implemented (even in synchronous systems). Hence, the paper provides us with the ?rst proof showing that consensus can be solved in anonymous systems with only partial synchrony (and a majority of correct processes).