XTo solve the problem, we start with a space whose store constrains the variables X, Y, and Z to the given domains. We also create three propagators imposing the constraints X7 Z
2 X - Z = 3 . Y
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The propagators for the disequations immediately write all their information into the store and disappear. The store then knows the domains
where![]()
Now propagation has reached a fixpoint. Thus, we continue with a first branching step. We choose to branch with the constraint X = 4. Figure 3 shows the resulting search tree.![]()
The space obtained by adding a propagator for X = 4 can be solved by propagation and yields the solution
X = 4 Y = 1 Z = 1The space obtained by adding a propagator for X
This time we branch with respect to the constraint X = 5.![]()
The space obtained by adding a propagator for X = 5 fails since X - Z = 3 . Y is inconsistent with the store obtained by adding X = 5.
The space obtained by adding a propagator for X 5
reaches a fixpoint immediately after this propagator
has written its information into the constraint store,
which then looks as follows:
Now we branch with respect to the constraint X = 6.![]()
The space obtained by adding a propagator for X = 6 can be solved by propagation and yields the solution
X = 6 Y = 1 Z = 3Finally, the space obtained by adding a propagator for X
X = 8 Y = 1 Z = 5An alternative to the propagate and branch method is a naive enumerate and test method, which would enumerate all triples (X, Y, Z) admitted by the initial domain constraints and test the constraints X
Andreas Rossberg 2006-08-28