On the complexity of basic abstractions to implement consensus
Résumé
Consensus is one of the central distributed abstractions. By enabling a collection of processes to agree on one of the values they propose, consensus can be used to implement any generic replicated service in a consistent and fault-tolerant way. Therefore, complexity of consensus implementations has become one of the most important topics in the theory of distributed computing. Several concurrent objects have been proposed as building blocks to implement obstruction-free consensus or wait-free consensus in distributed systems augmented with failure detectors or strong synchronization primitives.
In this paper we study an important subset of these objects: adopt-commit], conflict-detector], value-splitter and grafarius. We show that while some of these objects (adopt-commits and conflict-detectors) ensure a superset of the properties ensured by the others (value-splitter and grafarius), their space and individual step complexity is the same if implemented anonymously (the algorithm does not use process IDs). On the other hand, adopt-commit and conflict-detector objects have a larger complexity if we consider non anonymous implementations.