Doublet–triplet splitting problem

Vector clocks is an algorithm for generating a partial ordering of events in a distributed system and detecting causality violations. Just as in Lamport timestamps, interprocess 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 "smallest possible values" copy of the global clock-array is kept in each process, with the following rules for clock updates:

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.
• Each time a process prepares to send a message, it increments its own logical clock in the vector by one and then sends its entire vector along with the message being sent.
• 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).

The vector clocks algorithm was independently developed by Colin Fidge and Friedemann Mattern in 1988.

Partial ordering property

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

• $VC(x)$ denote the vector clock of event $x$, and $VC(x)_{z}$ denote 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:

• If $VC(a)<VC(b)$, then $a\to b\;$
• 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

• Almeida et al., introduced in 2008 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. You can find an implementation of ITC named itc4j here.

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

See also

• Lamport timestamps
• Matrix clocks
• Version vector
• Riak Vector Clocks http://docs.basho.com/riak/latest/theory/concepts/Vector-Clocks/

References

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External links

• Explanation of Vector clocks
• Fundamentals of Distributed Computing: A Practical Tour of Vector Clock Systems
• Timestamp-based vector clock implementation in Erlang
• Vector clock implementation in Objective-C
• Vector clock implementation in Erlang
• Why Vector Clocks are Hard