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vector clock : ウィキペディア英語版
vector clock
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:
* 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 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) 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 (\le VC(y)_z ) \and \exists z' (VC(x)_ < VC(y)_ )
*
* 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)_ < VC(y)_).
* 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)

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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