Version vector

A version vector is a mechanism for tracking changes to data in a distributed system, where multiple agents might update the data at different times. The version vector allows the participants to determine if one update preceded another (happened-before), followed it, or if the two updates happened concurrently (and therefore might conflict with each other). In this way, version vectors enable causality tracking among data replicas and are a basic mechanism for optimistic replication. In mathematical terms, the version vector generates a preorder that tracks the events that precede, and may therefore influence, later updates.
Version vectors maintain state identical to that in a vector clock, but the update rules differ slightly; in this example, replicas can either experience local updates (e.g., the user editing a file on the local node), or can synchronize with another replica:
Pairs of replicas, , , can be compared by inspecting their version vectors and determined to be either: identical (formula_2), concurrent (formula_3), or ordered (formula_4 or formula_5). The ordered relation is defined as: Vector formula_4 if and only if every element of formula_7 is less than or equal to its corresponding element in formula_8, and at least one of the elements is strictly less than. If neither formula_4 or formula_5, but the vectors are not identical, then the two vectors must be concurrent.
Version vectors or variants are used to track updates in many distributed file systems, such as Coda (file system) and Ficus, and are the main data structure behind optimistic replication.