Vector clock

Not to be confused with Version vector.

A vector clock is a data structure used for determining the partial ordering of events in a distributed system and detecting causality violations. Just as in Lamport timestamps, inter-process messages contain the state of the sending process's logical clock. A vector clock of a system of N processes is an array/vector of N logical clocks, one clock per process; a local "largest possible values" copy of the global clock-array is kept in each process.

Denote $VC_{i}$ as the vector clock maintained by process i, the clock updates proceed as follows:

Example of a system of vector clocks. Events in the blue region are the causes leading to event B4, whereas those in the red region are the effects of event B4.

• Initially all clocks are zero.
• Each time a process experiences an internal event, it increments its own logical clock in the vector by one. For instance, upon an event at process i, it updates $VC_{i}[i]\leftarrow VC_{i}[i]+1$.
• Each time a process sends a message, it increments its own logical clock in the vector by one (as in the bullet above, but not twice for the same event) and then the message piggybacks a copy of its own vector.
• Each time a process receives a message, it increments its own logical clock in the vector by one and updates each element in its vector by taking the maximum of the value in its own vector clock and the value in the vector in the received message (for every element). For example, if process Pj receives a message m from Pi, it updates by setting $VC_{j}\leftarrow max(VC_{j}[k]+1,VC_{i}[k]),\forall k$.

History

Without using the specific name "vector clock", the concept of a vector clock was first mentioned in a 1986 paper by Rivka Ladin and Barbara Liskov where they use the term "multipart timestamp". 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.

Partial ordering property

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

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

Properties:

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

Relation with other orders:

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

Other mechanisms

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

• In 2005, Agargwal and Garg created Chain Clocks, a system that tracks dependencies using vectors with size smaller than the number of processes and that adapts automatically to systems with dynamic number of processes.
• In 2008, Almeida et al. introduced Interval Tree Clocks. 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, 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.

See also

• Lamport timestamps
• Matrix clocks
• Version vector

External links

• 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