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ii) CQA q
MAX
glb
D,AC (
D
)=[ ,
u
]
, where
is the value returned by
OPT
( D,AC,
q
,
D
)
MAX
lub
and u returned by OPT
( D,AC,
q
,
D
)
.
Example 5.5. Consider the aggregate constraints
AC = 1 2 3 }
and the
-
MAX
query q 1 of our running example. The problem OPT MAX
glb
( D,AC,
q 1 ,
D
)
for ”Bal-
ance Sheet” example is obtained by considering the objective function
(
z 2
x 2 )+
(
z 12
x 12 )
over the inequalities in Fig. 5.1 augmented with the following inequali-
ties:
z 12
z 2
2 M
μ 2
0
z 2
z 12
2 M
μ 12
0
μ 2 + μ 1 2 =
1
x 2
M
μ 2
0
x 2
M
μ 2
0
x 12
M
μ 1 2
0
x 12
M
μ 12
0
z 2
x 2
2 M
· (
1
− μ 2 )
0
z 2 +
x 2
2 M
· (
1
− μ 2 )
0
z 12
x 12
2 M
· (
1
− μ 12 )
0
z 12 +
x 12
2 M
· (
1
− μ 12 )
0;
x 2
M
0;
x 2
M
0;
x 12
M
0
x 12
M
0;
x 2 ,
x 12 Z
μ 2 , μ 12 ∈{
0
,
1
}
 
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