<s>
Distributed	B-Application
constraint	I-Application
optimization	I-Application
(	O
DCOP	O
or	O
DisCOP	B-Application
)	O
is	O
the	O
distributed	B-Architecture
analogue	O
to	O
constraint	B-Application
optimization	I-Application
.	O
</s>
<s>
Distributed	B-Architecture
Constraint	O
Satisfaction	O
is	O
a	O
framework	O
for	O
describing	O
a	O
problem	O
in	O
terms	O
of	O
constraints	O
that	O
are	O
known	O
and	O
enforced	O
by	O
distinct	O
participants	O
(	O
agents	O
)	O
.	O
</s>
<s>
Importantly	O
,	O
each	O
variable	O
is	O
owned	O
by	O
an	O
agent	O
;	O
this	O
is	O
what	O
makes	O
the	O
problem	O
distributed	B-Architecture
.	O
</s>
<s>
Formally	O
,	O
a	O
DCOP	O
is	O
a	O
tuple	B-Application
,	O
where	O
:	O
</s>
<s>
Usually	O
,	O
only	O
few	O
values	O
of	O
are	O
non-zero	O
,	O
and	O
it	O
is	O
represented	O
as	O
a	O
list	O
of	O
the	O
tuples	B-Application
that	O
are	O
assigned	O
a	O
non-zero	O
value	O
.	O
</s>
<s>
Each	O
such	O
tuple	B-Application
is	O
called	O
a	O
constraint	O
.	O
</s>
<s>
It	O
is	O
also	O
not	O
necessarily	O
a	O
surjection	B-Algorithm
,	O
i.e.	O
,	O
some	O
agents	O
may	O
own	O
no	O
variables	O
.	O
</s>
<s>
A	O
value	O
assignment	O
is	O
a	O
pair	O
where	O
is	O
an	O
element	O
of	O
the	O
domain	B-Algorithm
.	O
</s>
<s>
Given	O
this	O
representation	O
,	O
the	O
"	O
domain	B-Algorithm
"	O
(	O
that	O
is	O
,	O
the	O
set	O
of	O
input	O
values	O
)	O
of	O
the	O
function	O
f	O
can	O
be	O
thought	O
of	O
as	O
the	O
set	O
of	O
all	O
possible	O
contexts	O
for	O
the	O
DCOP	O
.	O
</s>
<s>
Each	O
agent	O
has	O
a	O
single	O
variable	O
whose	O
associated	O
domain	B-Algorithm
is	O
of	O
cardinality	B-Application
(	O
there	O
is	O
one	O
domain	B-Algorithm
value	O
for	O
each	O
possible	O
color	O
)	O
.	O
</s>
<s>
For	O
each	O
vertex	O
,	O
there	O
is	O
a	O
variable	O
with	O
domain	B-Algorithm
.	O
</s>
<s>
The	O
distributed	B-Architecture
multiple	O
-	O
variant	O
of	O
the	O
knapsack	B-Algorithm
problem	I-Algorithm
is	O
as	O
follows	O
:	O
given	O
a	O
set	O
of	O
items	O
of	O
varying	O
volume	O
and	O
a	O
set	O
of	O
knapsacks	O
of	O
varying	O
capacity	O
,	O
assign	O
each	O
item	O
to	O
a	O
knapsack	O
such	O
that	O
the	O
amount	O
of	O
overflow	O
is	O
minimized	O
.	O
</s>
<s>
To	O
encode	O
this	O
problem	O
as	O
a	O
DCOP	O
,	O
for	O
each	O
create	O
one	O
variable	O
with	O
associated	O
domain	B-Algorithm
.	O
</s>
<s>
Completeness	O
-	O
complete	O
search	O
algorithms	O
finding	O
the	O
optimal	O
solution	O
,	O
vs.	O
local	B-Algorithm
search	I-Algorithm
algorithms	I-Algorithm
finding	O
a	O
local	O
optimum	O
.	O
</s>
<s>
Smart	B-Architecture
grid	I-Architecture
:	O
the	O
increase	O
in	O
price	O
of	O
electricity	O
in	O
loaded	O
hours	O
may	O
be	O
different	O
agents	O
.	O
</s>
