From the Happened-Before Relation to the Causal Ordered Set Abstraction

Several works in distributed systems have been designed based on the Happened-Before Relation (HBR). Most of these works intend to be efficient in their implementation by identifying and ensuring dependency constraints among single events. Even when the minimal causal dependencies among events have been clearly identified, the evolution of systems, which may involve a high number of processes and a high volume of transmitted data, calls for the need to design even more efficient approaches. This paper proposes the Causal Ordered Set Abstraction (CAOS) where the causally related events are arranged in sets that are strictly causally ordered. As for single events, CAOS establishes that any pair of resultant sets can be, and can only be, causally or concurrently related. We claim that our ordered set abstraction can be used to design more efficient algorithms based on the HBR principle. This assertion is based on two main properties. First, CAOS attains a consistent compact representation of a distributed computation. Second, as a consequence of the causal ordering of the events in the resultant sets, it is sufficient to verify only a pair of single events, one per each set, in order to determine whether these sets are causally or concurrently related, regardless of the cardinality of the sets.

► This paper presents the Causal Ordered Set Abstraction (CAOS).
► CAOS arranges in sets the causally related events of a distributed system.
► The resultant sets in CAOS are strictly causally ordered.
► CAOS attains a compact and consistent representation of a distributed computation.
► The causality between sets can be determined by comparing only their endpoints.