Decomposition method (constraint satisfaction): Difference between revisions

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Decomposition methods: The example instance did not match the decomposition. Two variables were swapped.
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This translation requires the maximal cliques of a chordal graph to be identified. However, this can bonebe done easily using the same ordering used for enforcing chordality. Since the parents of each node are all connected to each other, the maximal cliques are composed of a node (the maximal node of the clique in a max-cardinality ordering) and all its parents. As a result, these maximal cliques can be detected by considering each node with its parents.
 
The problem that results from this process has a join tree, and such a join tree can be obtained by using the same ordering of variables again. Proceeding from the last node to the first, every constraint is connected with the preceding constraint that shares more variables with it. Join-tree clustering can be seen as a decomposition method in which: