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[Part4] Element Constraint


Question 1: 1D Element: Domain Consistency

Assume an Element constraint for \(T[y]=z\), with:

  • \(D(y) = \{0,1,2,3,4\}\)
  • \(T = [5,5,5,10,8]\)
  • \(D(z) = \{5,10\}\)

What is the domain of \(y\) after a domain-consistent filtering?

Question 2: 2D Element: Domain Consistency

Assume an Element constraint for \(T[x][y]=z\), with:

  • \(D(x) = \{0,1,2\}\)
  • \(D(y) = \{3\}\)
  • \(T = [[1,8,9,6],[1,9,2,4],[9,8,9,8],[1,9,2,5]]\)
  • \(D(z) = \{2,...,6\}\)

What is the domain of \(z\) after a domain-consistent filtering?

Question 3: 1D Element: Domain Consistency

Assume an Element constraint for \(T[y]=z\), with:

  • \(D(y) = \{0,1,2,3,4\}\)
  • \(T = [5,5,5,10,8]\)
  • \(D(z) = \{5,6,7,8,9,10\}\)

What is the domain of \(z\) after a domain-consistent filtering?

Question 4: Stable Matching: Modeling

In the stable matching problem, the constraint "the company of the student of company c is c" is modeled with: