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Unformatted text preview: 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....
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This note was uploaded on 10/30/2009 for the course CS 221 at Stanford.
 '09
 KOLLER,NG

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