CS221 Exercise Set #3
1
CS 221
Exercise Set #3 : CSPs and Supervised Learning
1.
Job Shop Scheduling as a CSP
Consider the task of scheduling a set of tasks in a machine shop (e.g., for assembling an
airplane wing). Each task has a start time
Start
i
and a fixed duration
d
i
. We also have
sequencing constraints between operations.
If operation
i
precedes operation
j
, we can
write the constraint
Start
i
+
d
i
≤
Start
j
(1)
A second kind of constraint is the resource constraint. In the simple setting, we list for each
task
i
the set of resources that it requires
R
i
. (Resources include things like machines and
people needed to complete the task.) If two operations
i
and
j
require the same resource,
then we have the constraint that:
(
Start
i
+
d
i
≤
Start
j
)
∨
(
Start
j
+
d
j
≤
Start
i
)
(2)
For example, we might have several parts that need to be polished. The polishing machine
would be a resource that is needed for several operations.
Now, consider a more complex setting, where a given resource constraint for a task can be
fulfilled by several “actual” resources. For example, either Pat or Mike might be able to
polish a part. Note that the resources are not necessarily identical; for example, Pat might
be able to weld whereas Mike might not. More precisely, assume we have a set
R
of actual
resources. For each task
i
, the set of resource constraints is now defined by a set of sets
R
1
i
, . . . , R
k
i
, where each
R
ℓ
i
⊆ R
; in order for task
i
to be performed, it requires the use of
one resource in each
R
ℓ
i
. For example, our polishing task might be specified as
R
1
1
=
{
Pat,
Mike
}
,
R
2
1
=
{
machine1, machine2
}
, and
R
3
1
=
{
Jan,Tom
}
. This task can be accomplished
by assigning to it the resources Pat, machine2, and Tom. For simplicity, we assume that
two different sets
R
ℓ
i
and
R
m
i
are disjoint; e.g., we can’t have
R
3
1
=
{
Pat,Tom
}
.
Show how this task would be represented as a CSP. Specify exactly and formally what the
variables are and what the constraints are. Use a formal specification of the constraints,
along the lines of (1) and (2) above.
2.
CSP algorithms
This question will use CSP algorithms on a 6queens problem.
We use the formulation
described in class, where we have a variable
V
i
representing the row of the queen in column
i
. Remember that the 6queens problem requires that we place all 6 queens on the board
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 '09
 KOLLER,NG
 Maximum likelihood, Estimation theory, Likelihood function, Ri, Exercise Set, XX OXXXXX XX

Click to edit the document details