Commuting operations greatly simplify consistency in distributed systems. This paper focuses on designing for commutativity, a topic neglected previously. We show that the replicas of any data type for which concurrent operations commute converges to a correct value, under some simple and standard assumptions. We also show that such a data type supports transactions with very low cost. We identify a number of approaches and techniques to ensure commutativity. We re-use some existing ideas (non-destructive updates coupled with invariant identification), but propose a much more efficient implementation. Furthermore, we propose a new technique, background consensus. We illustrate these ideas with a shared edit buffer data type.
@cite_4 were the first to suggest the CRDT approach. They give the example of an array with a slot assignment operation. To make concurrent assignments commute, they propose a deterministic procedure (based on vector clocks) whereby one takes precedence over the other.
@cite_4
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As collaboration over the Internet becomes an everyday affair, it is increasingly important to provide high quality of interactivity. Distributed applications can replicate collaborative objects at every site for the purpose of achieving high interactivity. Replication, however, has a fatal weakness that it is difficult to maintain consistency among replicas. This paper introduces operation commutativity as a key principle in designing operations in order to manage distributed replicas consistent. In addition, we suggest effective schemes that make operations commutative using the relations of objects and operations. Finally, we apply our approaches to some simple replicated abstract data types, and achieve their consistency without serialization and locking.