Vector clock

Without using the specific name "vector clock", the concept of a vector clock was first mentioned[1] in a 1986 paper by Rivka Ladin and Barbara Liskov where they use the term "multipart timestamp".[2] To quote from page 31 of the Liskov/Ladin paper:

We solve this problem by using multipart timestamps, where there is one part for each replica. Thus, if there are n replicas, a timestamp t is

t = <t1, …, tn>

where each part is a positive integer. Since there will typically be a small number of replicas (e.g., 3 to 7), using such a timestamp is practical.

The term "vector clock" was first used independently by Colin Fidge and Friedemann Mattern in 1988.[3][4]

Vector clocks allow for the partial causal ordering of events. Defining the following:

• ${\displaystyle VC(x)}$ denotes the vector clock of event ${\displaystyle x}$, and ${\displaystyle VC(x)_{z}}$ denotes the component of that clock for process ${\displaystyle z}$.
• ${\displaystyle VC(x)<VC(y)\iff \forall z[VC(x)_{z}\leq VC(y)_{z}]\land \exists z'[VC(x)_{z'}<VC(y)_{z'}]}$
  • In English: ${\displaystyle VC(x)}$ is less than ${\displaystyle VC(y)}$, if and only if ${\displaystyle VC(x)_{z}}$ is less than or equal to ${\displaystyle VC(y)_{z}}$ for all process indices ${\displaystyle z}$, and at least one of those relationships is strictly smaller (that is, ${\displaystyle VC(x)_{z'}<VC(y)_{z'}}$).
• ${\displaystyle x\to y\;}$ denotes that event ${\displaystyle x}$ happened before event ${\displaystyle y}$. It is defined as: if ${\displaystyle x\to y\;}$, then ${\displaystyle VC(x)<VC(y)}$

Properties:

• Antisymmetry: if ${\displaystyle VC(a)<VC(b)}$, then ¬${\displaystyle (VC(b)<VC(a))}$
• Transitivity: if ${\displaystyle VC(a)<VC(b)}$ and ${\displaystyle VC(b)<VC(c)}$, then ${\displaystyle VC(a)<VC(c)}$ or if ${\displaystyle a\to b\;}$ and ${\displaystyle b\to c\;}$, then ${\displaystyle a\to c\;}$

Relation with other orders:

• Let ${\displaystyle RT(x)}$ be the real time when event ${\displaystyle x}$ occurs. If ${\displaystyle VC(a)<VC(b)}$, then ${\displaystyle RT(a)<RT(b)}$
• Let ${\displaystyle C(x)}$ be the Lamport timestamp of event ${\displaystyle x}$. If ${\displaystyle VC(a)<VC(b)}$, then ${\displaystyle C(a)<C(b)}$

• In 1999, Torres-Rojas and Ahamad developed Plausible Clocks,[5] a mechanism that takes less space than vector clocks but that, in some cases, will totally order events that are causally concurrent.

• In 2008, Almeida et al. introduced Interval Tree Clocks.[6][7][8] This mechanism generalizes Vector Clocks and allows operation in dynamic environments when the identities and number of processes in the computation is not known in advance.

• In 2019, Lum Ramabaja developed Bloom Clocks, [9] a probabilistic data structure whose space complexity does not depend on the number of nodes in a system. If two clocks are not comparable, the bloom clock can always deduce it, i.e. false negatives are not possible. If two clocks are comparable, the bloom clock can calculate the confidence of that statement, i.e. it can compute the false positive rate between comparable pairs of clocks.

• Lamport timestamps
• Matrix clocks
• Version vector

• Why Logical Clocks are Easy (Compares Causal Histories, Vector Clocks and Version Vectors)
• Explanation of Vector clocks
• Timestamp-based vector clock implementation in Erlang
• Vector clock implementation in Objective-C
• Vector clock implementation in Erlang
• Why Vector Clocks are Hard
• Why Cassandra doesn’t need vector clocks