<s>
A	O
version	B-Operating_System
vector	I-Operating_System
is	O
a	O
mechanism	O
for	O
tracking	O
changes	O
to	O
data	O
in	O
a	O
distributed	B-Architecture
system	I-Architecture
,	O
where	O
multiple	O
agents	O
might	O
update	O
the	O
data	O
at	O
different	O
times	O
.	O
</s>
<s>
The	O
version	B-Operating_System
vector	I-Operating_System
allows	O
the	O
participants	O
to	O
determine	O
if	O
one	O
update	O
preceded	O
another	O
(	O
happened-before	B-Operating_System
)	O
,	O
followed	O
it	O
,	O
or	O
if	O
the	O
two	O
updates	O
happened	O
concurrently	O
(	O
and	O
therefore	O
might	O
conflict	O
with	O
each	O
other	O
)	O
.	O
</s>
<s>
In	O
this	O
way	O
,	O
version	B-Operating_System
vectors	I-Operating_System
enable	O
causality	B-Application
tracking	O
among	O
data	O
replicas	O
and	O
are	O
a	O
basic	O
mechanism	O
for	O
optimistic	B-General_Concept
replication	I-General_Concept
.	O
</s>
<s>
In	O
mathematical	O
terms	O
,	O
the	O
version	B-Operating_System
vector	I-Operating_System
generates	O
a	O
preorder	O
that	O
tracks	O
the	O
events	O
that	O
precede	O
,	O
and	O
may	O
therefore	O
influence	O
,	O
later	O
updates	O
.	O
</s>
<s>
Version	B-Operating_System
vectors	I-Operating_System
maintain	O
state	O
identical	O
to	O
that	O
in	O
a	O
vector	B-Operating_System
clock	I-Operating_System
,	O
but	O
the	O
update	O
rules	O
differ	O
slightly	O
;	O
in	O
this	O
example	O
,	O
replicas	O
can	O
either	O
experience	O
local	O
updates	O
(	O
e.g.	O
,	O
the	O
user	O
editing	O
a	O
file	O
on	O
the	O
local	O
node	O
)	O
,	O
or	O
can	O
synchronize	O
with	O
another	O
replica	O
:	O
</s>
<s>
After	O
synchronization	O
,	O
the	O
two	O
replicas	O
have	O
identical	O
version	B-Operating_System
vectors	I-Operating_System
.	O
</s>
<s>
Pairs	O
of	O
replicas	O
,	O
,	O
,	O
can	O
be	O
compared	O
by	O
inspecting	O
their	O
version	B-Operating_System
vectors	I-Operating_System
and	O
determined	O
to	O
be	O
either	O
:	O
identical	O
(	O
)	O
,	O
concurrent	O
(	O
)	O
,	O
or	O
ordered	O
(	O
or	O
)	O
.	O
</s>
<s>
Version	B-Operating_System
vectors	I-Operating_System
or	O
variants	O
are	O
used	O
to	O
track	O
updates	O
in	O
many	O
distributed	O
file	O
systems	O
,	O
such	O
as	O
Coda	B-Application
(	O
file	O
system	O
)	O
and	O
Ficus	O
,	O
and	O
are	O
the	O
main	O
data	O
structure	O
behind	O
optimistic	B-General_Concept
replication	I-General_Concept
.	O
</s>
<s>
Concise	O
Version	B-Operating_System
Vectors	I-Operating_System
allow	O
significant	O
space	O
savings	O
when	O
handling	O
multiple	O
replicated	O
items	O
,	O
such	O
as	O
in	O
directory	O
structures	O
in	O
filesystems	O
.	O
</s>
<s>
Interval	O
Tree	O
Clocks	O
generalize	O
version	B-Operating_System
vectors	I-Operating_System
and	O
vector	B-Operating_System
clocks	I-Operating_System
and	O
allows	O
dynamic	O
numbers	O
of	O
replicas/processes	O
.	O
</s>
<s>
Bounded	O
Version	B-Operating_System
Vectors	I-Operating_System
allow	O
a	O
bounded	O
implementation	O
,	O
with	O
bounded	O
size	O
counters	O
,	O
as	O
long	O
as	O
replica	O
pairs	O
can	O
be	O
atomically	O
synchronized	O
.	O
</s>
<s>
Dotted	O
Version	B-Operating_System
Vectors	I-Operating_System
address	O
scalability	O
with	O
a	O
small	O
set	O
of	O
servers	O
mediating	O
replica	O
access	O
by	O
a	O
large	O
number	O
of	O
concurrent	O
clients	O
.	O
</s>
