<s>
A	O
vector	B-Operating_System
clock	I-Operating_System
is	O
a	O
data	B-General_Concept
structure	I-General_Concept
used	O
for	O
determining	O
the	O
partial	O
ordering	O
of	O
events	O
in	O
a	O
distributed	B-Architecture
system	I-Architecture
and	O
detecting	O
causality	B-Application
violations	O
.	O
</s>
<s>
Just	O
as	O
in	O
Lamport	B-Operating_System
timestamps	I-Operating_System
,	O
inter-process	O
messages	O
contain	O
the	O
state	O
of	O
the	O
sending	O
process	O
's	O
logical	B-Operating_System
clock	I-Operating_System
.	O
</s>
<s>
A	O
vector	B-Operating_System
clock	I-Operating_System
of	O
a	O
system	O
of	O
N	O
processes	O
is	O
an	O
array/vector	O
of	O
N	O
logical	B-Operating_System
clocks	I-Operating_System
,	O
one	O
clock	O
per	O
process	O
;	O
a	O
local	O
"	O
largest	O
possible	O
values	O
"	O
copy	O
of	O
the	O
global	O
clock-array	O
is	O
kept	O
in	O
each	O
process	O
.	O
</s>
<s>
Denote	O
as	O
the	O
vector	B-Operating_System
clock	I-Operating_System
maintained	O
by	O
process	O
,	O
the	O
clock	O
updates	O
proceed	O
as	O
follows	O
:	O
</s>
<s>
Each	O
time	O
a	O
process	O
experiences	O
an	O
internal	O
event	O
,	O
it	O
increments	O
its	O
own	O
logical	B-Operating_System
clock	I-Operating_System
in	O
the	O
vector	O
by	O
one	O
.	O
</s>
<s>
Each	O
time	O
a	O
process	O
sends	O
a	O
message	O
,	O
it	O
increments	O
its	O
own	O
logical	B-Operating_System
clock	I-Operating_System
in	O
the	O
vector	O
by	O
one	O
(	O
as	O
in	O
the	O
bullet	O
above	O
,	O
but	O
not	O
twice	O
for	O
the	O
same	O
event	O
)	O
and	O
then	O
the	O
message	O
piggybacks	O
a	O
copy	O
of	O
its	O
own	O
vector	O
.	O
</s>
<s>
Each	O
time	O
a	O
process	O
receives	O
a	O
message	O
,	O
it	O
increments	O
its	O
own	O
logical	B-Operating_System
clock	I-Operating_System
in	O
the	O
vector	O
by	O
one	O
and	O
updates	O
each	O
element	O
in	O
its	O
vector	O
by	O
taking	O
the	O
maximum	O
of	O
the	O
value	O
in	O
its	O
own	O
vector	B-Operating_System
clock	I-Operating_System
and	O
the	O
value	O
in	O
the	O
vector	O
in	O
the	O
received	O
message	O
(	O
for	O
every	O
element	O
)	O
.	O
</s>
<s>
For	O
example	O
,	O
if	O
process	O
receives	O
a	O
message	O
from	O
,	O
it	O
first	O
increments	O
its	O
own	O
logical	B-Operating_System
clock	I-Operating_System
in	O
the	O
vector	O
by	O
one	O
and	O
then	O
updates	O
its	O
entire	O
vector	O
by	O
setting	O
.	O
</s>
<s>
Lamport	O
originated	O
the	O
idea	O
of	O
logical	O
Lamport	B-Operating_System
clocks	I-Operating_System
in	O
1978	O
.	O
</s>
<s>
However	O
,	O
the	O
logical	B-Operating_System
clocks	I-Operating_System
in	O
that	O
paper	O
were	O
scalars	O
,	O
not	O
vectors	O
.	O
</s>
<s>
The	O
generalization	O
to	O
vector	B-Operating_System
time	I-Operating_System
was	O
developed	O
several	O
times	O
,	O
apparently	O
independently	O
,	O
by	O
different	O
authors	O
in	O
the	O
early	O
1980	O
's	O
.	O
</s>
<s>
The	O
papers	O
canonically	O
cited	O
in	O
reference	O
to	O
vector	B-Operating_System
clocks	I-Operating_System
are	O
Colin	O
Fidge	O
’s	O
and	O
Friedemann	O
Mattern	O
’s	O
1988	O
works	O
,	O
</s>
<s>
as	O
they	O
(	O
independently	O
)	O
established	O
the	O
name	O
"	O
vector	B-Operating_System
clock	I-Operating_System
"	O
and	O
the	O
mathematical	O
properties	O
of	O
vector	B-Operating_System
clocks	I-Operating_System
.	O
</s>
<s>
Vector	B-Operating_System
clocks	I-Operating_System
allow	O
for	O
the	O
partial	O
causal	O
ordering	O
of	O
events	O
.	O
</s>
<s>
denotes	O
the	O
vector	B-Operating_System
clock	I-Operating_System
of	O
event	O
,	O
and	O
denotes	O
the	O
component	O
of	O
that	O
clock	O
for	O
process	O
.	O
</s>
<s>
Let	O
be	O
the	O
Lamport	B-Operating_System
timestamp	I-Operating_System
of	O
event	O
.	O
</s>
<s>
In	O
1999	O
,	O
Torres-Rojas	O
and	O
Ahamad	O
developed	O
Plausible	O
Clocks	O
,	O
a	O
mechanism	O
that	O
takes	O
less	O
space	O
than	O
vector	B-Operating_System
clocks	I-Operating_System
but	O
that	O
,	O
in	O
some	O
cases	O
,	O
will	O
totally	O
order	O
events	O
that	O
are	O
causally	O
concurrent	O
.	O
</s>
<s>
This	O
mechanism	O
generalizes	O
Vector	B-Operating_System
Clocks	I-Operating_System
and	O
allows	O
operation	O
in	O
dynamic	O
environments	O
when	O
the	O
identities	O
and	O
number	O
of	O
processes	O
in	O
the	O
computation	O
is	O
not	O
known	O
in	O
advance	O
.	O
</s>
<s>
In	O
2019	O
,	O
Lum	O
Ramabaja	O
developed	O
Bloom	O
Clocks	O
,	O
a	O
probabilistic	O
data	B-General_Concept
structure	I-General_Concept
whose	O
space	O
complexity	O
does	O
not	O
depend	O
on	O
the	O
number	O
of	O
nodes	O
in	O
a	O
system	O
.	O
</s>
