Constraint Satisfaction Problems
(CSP)
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Constraint Satisfaction Problems
(CSP)
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● X1, X2, …, Xn
● D1, D2, … Dn Di = {v1, …, vk}
● C1, C2, …, Cm
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○ X1, X2 X1 > X2>
○ D1 = D2 = {1, 2, 3},
< X1, X2
● Ci
X1≠ X2
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Vi,j , i, j ∈ {1, . . ., 9}
Di,j = {1, . . ., 9}
● CR: V3,5 , {2, 4}>
● CC: V3,5 , {1, 3, 4, 5, 8}>
● CG: V3,5 , {1, 2, 3, 4, 6,
9}>
● V3,5 = {4}
V3,5
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● Di
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○ Alldiff
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Constraint Satisfaction Problems
(CSP)
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○ Xi Di Xi
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■ DSA DSA
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● Xi Xj Di
Dj Xi , Xj
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● Xi , Xj
○ v Xi
■ Xj v
● v Xi
● Xi Xj Di
Dj Xi , Xj
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● Xi Xj Di
Dj Xi , Xj
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● Xi Xj Di
Dj Xi , Xj
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● Xi Xj Di
Dj Xi , Xj
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● Xi , Xj Xk
Xi= a , Xj= b Xk
Xi , Xk Xj , Xk
Constraint Satisfaction Problems
(CSP)
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Xi
Xj
Xi Xj
● Xi
● Xi
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● Xj
Xi
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○ n n-1
○ 2 × n × (n-1) O(n2)
● O(n2d3)
○ d Xi , Xj O(d
2)
○ Xi , Xj d
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k
● k k-1
k-1
kth
● k k j < k
j
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● Xi
Di
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